What happens to money when you pay electronically, and does it actually move between banks?

There is no physical transfer of money, as the money you have, is electronically assigned.

The value transfer between banks, is simply the two banks agreeing to adjust their ledgers, sometimes with the aid of intermediaries. In the crudest of sense think of nothing more than digital numbers moving between banks.

To understand how money moves, the following two answers might be helpful:

• Faisal Khan's answer to How does the settlement of payments work in banks? Specifically, how do payment systems that are connected to multiple banks actually settle the amount between two banks?
  
• Faisal Khan's answer to How does money transfer between banks and different countries work?