The Nintendo 3DS is a powerful multitasking beast, besting the efforts of many handhelds and consoles before it. If you don't want to quit out of your game, you can use one of the four highlighted icons to perform additional tasks on top of your game after pressing the Home button.
For example, want to jot down some important notes during a game? Don't ruin the last few pages of your instruction booklet. Instead, tap the pencil icon to access Game Memo, an app that lets you draw and write anything you want. (It looks a lot like Pictochat.) Once you're done, you can save your image to the SD card.
Is your system notification LED flashing orange? That means one of your Wi-Fi connected friends is online. Tap the smiley face button to see what your friends are playing. The speech bubble icon will give you insight into all of your Spot Pass and Street Pass activity, letting you know when you've downloaded something new. Finally, the internet browser (available via firmware update) should let you research some GameFAQs and read some Joystiq while you take a break from raiding some faces.