[Warning; there is nothing to learn from reading this, it's just ramble.]
I've been using bitcoin for a good while already, but I haven't really put in the effort to get a good understanding of everything until today. I spent hours reading the Satoshi paper and the wiki. Cool story, right? Here's some stuff I got out of it:
The whole mining process, and how it self-regulates and requires little network coordination. Pretty cool. How difficulty is computed, and how it relates to target.
What's inside a block, and the structure of a block header, and how the chain is linked together. How that provides a "distributed timestamp server". And how impossibly difficult it would be to modify something in an old block. Very neatly designed, and now I understand how "lite" clients work and how they only need 80 bytes per block instead of the whole thing. Also the potential for pruning, and I noticed a cool BIP about stratization that makes me feel more comfortable about future scaling.
How transactions work, and what's inside them. Inputs and outputs. I finally understand how a coin can be split to pieces and different pieces can be combined into bigger values, all without fragmentation. And the transaction fee is just what's left after the all the inputs are subtracted from all the outputs, very elegant.
Script! How cool, so many possibilities. And so many opcodes that are disabled, probably best for now.
Generally how the peer-to-peer network works, what kind of messages are exchanged, and how they are propagated etc.