To expand on the above post:
For the most part, if an app is designed to continue to use CPU after it's not the active window, you'll see an icon for that app in your notification bar up top, telling you that it's still running. Apps like music players, navigation, and some online games are good examples.
However, there are apps designed to sync periodically in the background. These syncs often trigger a sync icon in the notification bar, but not always. If you're concerned about battery life, check your sync list and disable stuff you don't care about. Go to Settings > Accounts & Sync to see what apps are on auto-sync.