What is a "Change Address", and why is it useful?
The concept of change addresses is a feature not of the Bitcoin protocol, but of a Bitcoin client. It is implemented not only in Electrum but in most Bitcoin clients, including the original "Satoshi" Bitcoin client.
How it works:
Whenever your Bitcoin client (e.g. Electrum) sends Bitcoins from your wallet's address "A" to a foreing address "B", a new change address "C" is created by Electrum and added to your wallet.
Example: Address "A" has 20 BTC. Electrum sends 9 BTC from "A" to "B". The change (20-9 = 11 BTC) is sent to the "change address" "C". For this purpose, address "C" is created by Electrum at this moment and added to your wallet.
Exception: If all the Bitcoins of "A" are sent to "B", there is no need for creating a change address "C".
Actually, Bitcoin clients can also work without change addresses. In this case, the change would be sent back to "A" instead of the new address "C".
Why the concept of "change addresses" is useful:
Using a new change address makes it more difficult for other people (by analyzing the blockchain) to track how many Bitcoins you have or where you're spending them.
It also conceals which output is the "spend" and which is the "change".
Thanks, that's a very helpful explanation!