The Theory Behind Bitcoin in a Nutshell: Based on Satoshi Nakamoto's White Paper

Bitcoin is a Peer-to-Peer Electronic Cash System.

What does a peer-to-peer electronic cash system allow?   A peer-to-peer version of electronic cash would allow online payments to be sent directly from one person to another without going through financial institutions. (ex. banks).

A digital signature provides a solution to online payments, but the benefits would be lost if a trusted third party is needed to prevent double-spending.  A solution to this double-spending is a peer-to-peer network.

The network timestamps the transactions by hashing them into an ongoing chain of hash-based proof of work, which forms a record that cannot be changed without redoing the initial proof of work. 

What exactly is hashing?  It is the transformation of a string of characters into a usually shorter fixed-length value or key that represents the original string. It is used to index and retrieve items in a database because it is faster to find the item using the shorter hashed key than to find it using the original value.

The longest chain serves as proof of the sequence of events shown on the chain, it shows that it came from the largest pool of CPU power.  The CPU power controlled by the nodes (miners); not attacking the network, generate the longest chain and outruns any potential attackers to the chain.

The peer-to-peer network does not require a lot of structure.

Work done by the nodes (miners) are broadcasted on the chain.  Nodes join and leave the network at will.  The hash they leave behind is proof of their work.

Based on my interpretation of Satoshi Nakamoto's White Paper.