Pressing the PS button while playing a PlayStation Vita game will bring up the system's OS. You can access a number of features, including your music collection, your friend list, and the system's Twitter client, and when you're done, you can jump right back into your current game.
One feature you won't be able to access is the system's web browser. Impress Watch updated its Random Tracking feature about Vita's multimedia features (see this story for a summary) with a correction about the web browser component. The story had originally said that the browser can be opened up while you've paused a game. Following the story's publication, Sony contacted the site and said that this is not the case. Initially, the Vita will not be able to run the browser simultaneously with a game. In other words, if you want to open the browser, you'll have to exit your game entirely.
The wording of Sony's correction suggests that this is an issue that will be fixed via an update following the system's release.