The Paper

On this page, I will try to dissect the best I could Satoshi Nakamoto's paper Bitcoin: A Peer-to-Peer Electronic Cash System in a way an average person can understand it. For the full context of Nakamoto's paper, you can read it via bitcoin.org.

Obviously, from its title itself, Bitcoin is an electronic cash system. It is electronic because it requires the use of an electronic equipment such as a computer. It is a system because it comprises multiple sets of processes and procedures based on principles, and affected by multiple factors, compiled into one complex whole to function as a tool or utility to aid humans in performing certain tasks in a more convenient and fast way. It is cash, therefore, it involves money or medium of exchange, in general.

The Abstract

The first line of the paper's abstract says:

A purely peer-to-peer version of electronic cash would allow online payments to be sent directly from one party to another without going through a financial institution.

You can understand peer-to-peer to mean direct or one-on-one, ie without the need of a middleman, in bitcoin's case, a financial institution. As the abstract suggests, bitcoin will allow you to pay online even if you do not have a bank account, a credit card, or an account with a payment gateway that all charge you with transaction fees and other financial charges.

If bitcoin does not need a financial institution to meddle through your commerce, it means that you can put up a business, such as an online store, and receive bitcoins as payments without the need of a bank to approve or disapprove your credit standing, a credit card company to allow you to accept credit card payments, or a payment gateway that requires a credit card or a bank account.

Digital signatures are part of the solution...

Currently, to verify a legitimate transaction online, your credit card guarantees the veracity of your transaction. With bitcoin, your digital signature guarantees the legitimacy of your transaction.

... but the main benefits are lost if a trusted third party is still required to prevent double-spending.

The abstract emphasizes that there should be no third party involved in any bitcoin transaction even just to prevent double-spending. Therefore, how can bitcoin prevent double-spending?

We propose a solution to the double-spending problem using a peer-to-peer network. The network timestamps transactions by hashing them into an ongoing chain of hash-based proof-of-work, forming a record that cannot be changed without redoing the proof-of-work. 

So, there is a network exclusive for people with bitcoin. It is peer-to-peer, therefore, it does not require a central server. Every transaction is hash-based (encrypted hash codes) that includes the details of the transaction, a timestamp and a unique digital signature, making every bitcoin transaction absolutely unique.

... ongoing chain of hash-based proof-of-work, forming a record that cannot be changed without redoing the proof-of-work. The longest chain not only serves as proof of the sequence of events witnessed, but proof that it came from the largest pool of CPU power.

All bitcoin transactions, from the very first to the most recent one a second ago, are recorded chronologically in a virtual ledger called proof-of-work. It is ongoing because it is always updated each time a transaction occurs. The network of bitcoin users makes the largest pool of CPU power.

... nodes can leave and rejoin the network at will, accepting the longest proof-of-work chain as proof of what happened while they were gone.

Bitcoin users are referred to as nodes [who] can leave and rejoin the [Bitcoin] network at will. In computer lingo, a node is a data point, such as a computer or a device, in a network.

The Paper's Introduction

Bitcoin System Defined

In the paper's introduction, Bitcoin is defined as ~

... an electronic payment system based on cryptographic proof instead of trust, allowing any two willing parties to transact directly with each other without the need for a trusted third party.

Bitcoin is intended to be used as an electronic payment system. It is fully cryptographic, which means that every character is encrypted. Unlike other systems, texts such as user inputs and interface instructions, are written and readable in popular languages that you are familiar with. To understand what is encrypted, your password is.

How safe is Bitcoin?

The system is secure as long as honest nodes collectively control more CPU power than any cooperating group of attacker nodes.

Nodes refer to bitcoin users who are members of the network. It is possible that some users may have malicious intention to damage or hack the system. But so long as the network comprises more honest users than bad ones, Bitcoin is safe and secure. For that reason, bitcoin expects every user to be honest.

What does it mean to say that Bitcoin is not based on trust?

Bitcoin is based on cryptographic proof instead of trust. In financial transactions that involve a third party who mediate between two transacting parties, trust plays a very important factor to complete the transaction. The 3rd party mediator guarantees both the buyer and the seller that they can trust each other -- that he is a legitimate seller and that buyer is a good payer. With Bitcoin, the network guarantees the seller that she will be paid because the transaction can only be consummated upon payment with bitcoin. Unfortunately, in case of an online transaction, Bitcoin does not guarantee the paying customer that he will receive the right product or services. If such case occurs, there is no third party who can mediate between the paying customer and the merchant involved.

Does Bitcoin guarantee the paying customer to receive the right product or services?

No. Like in any online transaction, there is no guarantee that the customer will receive the right product or service. To ensure that customers are protected, merchants provide money-back guarantees, refund policies, and after-sales support. 

What Motivated Satoshi To Invent Bitcoin

The introduction of the paper states what made him write Bitcoin. In systems analysis, this is what we call problem definition. The following enumerates the weaknesses of the present e-commerce system (in absence of Bitcoin).

1. E-commerce or commerce on the Internet relies on financial institutions to serve as a trusted 3rd party to mediate between the buyer and the seller. It makes the buyer happy because he knows that his money goes to a legit seller. Likewise, it makes the seller happy because the 3rd party ensures that he will receive payment. The system works but not without weaknesses.
2. Transactions are reversible. Reversing transactions means no-sale, refund of payment, and additional cost to the seller – a sad face for the seller. Who would like to incur additional cost for a no-sale? Moreover, well and good, in a reversible transaction, if the goods can be returned to the seller by the buyer, but not very good if the object of the sale is in the form of service.
3. Trust plays a very significant role in e-commerce. For that reason, merchants are wary of their customers. They need to require more information from their customers to ensure that they are transacting with a trusted person. As a result, customers are self-obliged to divulge more information about them.
4. Fraud is unavoidable. No buyer would want to give money for nothing; likewise, no seller would want to lose their products for nothing.

What is Bitcoin In A Nutshell

1. It is an electronic cash system.
2. It is a network of bitcoin users.
3. It is a solution to solve the weaknesses of e-commerce.
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What Bitcoin (and other virtual currencies) Does

1. It allows you to make financial transactions online even if you do not have a credit or debit card. In case of using a payment gateway that honors bitcoin, neither that you have to prove that you have funds in a bank.
2. It allows you to receive payment directly from the buyer.
3. It guarantees the merchants that they are paid properly, eliminating the possibility of fraudulent payment. This is the reason why Bitcoin does not need trust. Whoever you are dealing with, you will surely get your money.
4. Though a bitcoin transaction is irreversible, it does not mean, in case of returns or money-back guarantee settlement, that customers cannot ask for a refund. The refund can be made with another bitcoin transaction. 
5. 
   

What Bitcoin (and Other Cryptocurrencies) Does Not

1. It does not need a credit card or a payment gateway, such as PayPal, unless the payment gateway accepts bitcoin; nevertheless, it is not necessary.
2. It does not require you to have a bank account, or to prove that you funds in a bank.
3. Though a bitcoin transaction protects merchants from a fraudulent payment, it does not protect the buyers from scam. In this case, the buyers must be wary of the e-commerce sites they enter into.
4. Bitcoin does not need trust in a sense that whoever your customer is, when he pays with bitcoin, the merchant gets his money's worth.
5. Bitcoin does not fall under the category digital payments.

Bitcoin Advantages

1. You don't need a credit card or a bank account to transact in bitcoin. Likewise, you don't need a payment gateway to transact in bitcoin; however, you may opt to use a payment gateway that accepts bitcoin.
2. Transactions you make are always proofed with your digital signature.
3. It does not require a central server making bitcoin hack-proof for the reason that, if there is no central server, the bad boys have nothing and nowhere to hack.
4. All bitcoin transactions are encrypted.
5. All bitcoin transactions are chained (recorded) in one virtual ledger.