Here's a good explanation
. Here's a good link from that link
Unless the app was designed to stay running, Background State Apps, or is poorly written it won't drain the battery in the background. It will free up RAM but there is no real advantage to that, if the OS needs more RAM it will selectively purge it. I imagine FIFO. Unless it is a Background State App it won't be using CPU/battery.
I had one app for finding restaurants that stayed active, using network data. The Location Services arrow in the upper right was always on so I went through the list of recents and found the app causing it by doing the procedure Papa outlined.
The advantage to keeping them open and stored in RAM is that they launch quicker.
You can quit all at once on the iPhone if it's jail broken.