Stupid question re: "script," "unspent outputs," and the divisibility of bitcoin

Hi All,

I have a stupid question: I don't understand how one bitcoin can be divided into satoshis.

Based on my basic understanding of how bitcoin works, it seems like each bitcoin is associated with an address (a hash of someone's public key?) in the public ledgor (the block chain?). If this association happens at the coin level, how can a bitcoin be divided into satoshis that can be associated with different addresses?

The whitepaper suggests it has to do with "script," "inputs" and "outputs." But my brain explodes when I read this on the Bitcoin wiki:

Quote

Bitcoin uses a scripting system for transactions. Forth-like, Script is simple, stack-based, and processed from left to right. It is purposefully not Turing-complete, with no loops.

WTF?!

Can someone please point me to resources on bitcoin divisibility that are more easily understandable? Thanks!