Q: IOS 7.02 update...feature to close open apps.

Double tap Home button. Swipe previews upwards - not small icons. Tap Home button to close.

Very few apps actually remain "open" and consume any phone resrouces or battey,  Most in the recently opened list are frozen, and there's not need to routinely "close" them.

iOS: Understanding multitasking

Swipe previews upwards - not small icons

Swiping UP either icons or preview works and can do 2 at a time

Actually, there was a tutotial which appeared after activating the update.

Only a few types of apps actually "run" in the background - audio streaming and navigation in particular.  A few other types will run for a short period to complete a task started before closing

Note that in iOS 7 there is a new feature to allow "Background App Refresh"  These can be globally or individually disabled to conserve battery:

Settings > General > Background App Refresh >