You have two choices for transferring and backing up Vita content, including photos, music, game saves, and downloaded games. You can either connect it to a PC (and, later, Mac -- the app isn't available as of the Japanese launch, to my irritation) with the "Content Manager Assistant" installed, which just enables the computer to read the Vita like a hard drive, or you can connect it to a PS3. The USB adapter is the same cable that goes from the Vita to the AC adapter.
In both cases, the actual movement of data is done from the Vita, in its own "Content Manager Assistant" app. The PS3 displays only the above screen. I plugged the handheld into the PS3, moved some photos around (the Shadows of the Damned and ... Hot Pockets promotional backgrounds, and 3D Dot Game Heroes screens being all I had).
You'll notice that the "music" and "photos" pages look slightly different. When you open up those areas to browse, it actually opens up the Vita's separate "Photo" and "Music" apps, leaving the Content Manager running in the background.