The Recent Apps button is Google's answer to easy multitasking on a tablet. Tablet screens are pretty small relative to most notebooks, so it's hard to have more than one window open at once. That doesn't mean you don't want more than one app to run at a time, and it doesn't mean you don't want to bounce from app to app occasionally.
For instance, assume you're writing an email to your boss. You'll want to quickly check your calendar to make sure your schedule is clear, and then verify some research on the Web. You can check the dates and then bounce back to your open email letter by using the Recent Apps button. Follow these steps to do so:
TIP: Tilt your screen to Portrait mode to see more app previews.