Multitasking gestures are quick, multitouch shortcuts for navigating around your iPad. You can enable or disable them in Settings (to avoid, for example, swiping in Fruit Ninja and suddenly ending up in Mail). When they're on, however, and you're used to using them, you can really fly between your iPad apps.
Some things are just easier to show rather than tell. Here's a quick video highlighting what the gestures are and what they look like when you do them.
Here's the full list of available gestures.
Swipe right with four fingers to switch move from the current app to the next app (according to the order presented in the Fast App Switcher)
5 Pinch with four fingers to exit an app and return to the Home screen (like clicking the Home button)
Think of gesture navigation as the keyboard shortcuts of the Home screen, or as the alt+tab or cmd+tab of app switching. A way to get around quickly when you need to.