A few minor suggestions (I'll highlight what I changed):
From the how it works page:
The basics for a new user:
As a new user, you only need to choose a wallet that you will install on your computer or on your mobile phone. Once your wallet is created, you have your first Bitcoin address and you can create more whenever you need one. You can disclose one of your Bitcoin addresses to your friends so that they can pay you. The same way, you can pay your friends if they give you their addresses. In fact, this is pretty similar to how email works. So all that is left to do that this point is to buy a few Bitcoins and to keep them safe. As a user, you are not required to understand the rest of the technical details.
As a new user, you only need to choose a wallet that you will install on your computer or on your mobile phone. Once you have your wallet installed, it will automatically generate your first Bitcoin address and you can create more whenever you need one. You can disclose one of your Bitcoin addresses to your friends so that they can pay you or vice versa, you can pay your friends if they give you their addresses. In fact, this is pretty similar to how email works. So all that is left to do at this point is to get some bitcoins and to keep them safe. In order to start using Bitcoin, you are not required to understand the rest of the technical details.
Blockchain:
The entire Bitcoin network relies on the blockchain. The blockchain is a shared public transaction log, in chronological order. All confirmed transactions are included in the blockchain with no exception so that new transactions can be verified to be spending bitcoins that are actually owned by the spender. The integrity of the blockchain is enforced with cryptography.
The entire Bitcoin network relies on the blockchain. The blockchain is a shared public chronological log of all past transactions. All valid transactions are included in the blockchain with no exception so that it can be verified the new transactions are spending bitcoins that are actually owned by the spender. The validity of the blockchain itself is determined with cryptography.
Transaction:
A transaction is a transfer of value between Bitcoin addresses that gets included in the blockchain. Bitcoin wallets keep a secret piece of data called a private key for each Bitcoin address. Private keys are used to sign transactions, providing a mathematical proof that they come from the owner of the addresses. The signature also prevents the transaction from being altered by anybody once it has been issued. All transactions are broadcast between users and confirmed by the network in the following minutes, through a process called mining.
A transaction is a transfer of bitcoins between Bitcoin addresses. Bitcoin wallets keep a secret piece of data called a private key for each Bitcoin address. Private keys are used to sign transactions, providing a mathematical proof of ownership for the bitcoins being sent. The signature also prevents the transaction from being altered by anybody once it has been carried out. All valid transactions are broadcasted between users and confirmed by the network through a process called mining in the following minutes.
Mining:
Mining is a distributed consensus system that is used to include and confirm waiting transactions in the blockchain. It enforces a chronological order in the blockchain, protects the neutrality of the network, and stops different computers disagreeing on the state of the system. To be confirmed, transactions must be packed in a block that fits very strict cryptographic rules that will be verified by the network. These rules prevent any previous block from being modified because it would invalidate all following blocks. It creates the equivalent of a competitive lottery that prevents any individual from easily adding new blocks consecutively in the blockchain. This way, no individuals can control what is included in the blockchain or replace parts of the blockchain and roll back their own spends.
Mining is a distributed consensus system that is used to include new transactions into the blockchain thereby confirming they are valid. It determines a chronological order in the blockchain, protects the decentralization of the network, and allows different computers part of the network to agree on the state of Bitcoin. In order to be confirmed, transactions must be packaged into blocks that fit very strict cryptographic rules which allow the network to determine the validity of those blocks. These rules prevent any previous block from being modified because doing so would invalidate all the following blocks. Mining also creates the equivalent of a competitive lottery that prevents any individual from easily adding new blocks consecutively into the blockchain. This way, no individual or a small group of individuals can control what is included into the blockchain or replace parts of the blockchain and roll back their own spends or spend bitcoins they don't own.