You might think that, since the PS Vita is the PSP's successor, managing and transferring games, photos, and other content would be pretty much the same. But just as the PS Vita got a brand-new user interface completely unlike the PSP's and PS3's XMB, the way you'll access and transfer content is different, too.
Out With the Old
Transferring content to and from a PSP was a simple drag-and-drop process that involved hooking your PSP up to a computer via a USB cable and treating it just like an external drive. As long as you had the correct file structure on your PSP's memory stick, you were good to go on a Windows or Mac. If you wanted something a little more like media management software, you could download Sony's Media Go software free, and use it for everything from managing content on your PC, to buying and downloading from the PlayStation Store, to transferring content back and forth from a PSP. The biggest drawback was that it's Windows only.
It's also possible to transfer content such as games downloaded from the PlayStation Store to a PSP from a PS3, essentially by connecting the two via a USB cable, navigating to the desired game on the PS3's XMB, selecting it, and selecting the option to transfer. In both of these scenarios, the PSP is treated more or less just like any other external storage device.
PS Vita Content Manager Assistant
With the PS Vita, you will no longer be able to transfer anything by the drag-and-drop method. There is speculation that this is an attempt to reduce piracy.
Content Manager Assistant for PlayStation is a computer application that enables data transfer between a PlayStation Vita system or PlayStation TV system and a computer. By installing the application on your computer, you can do things like copy content from your computer to your PS Vita system/PS TV system and back up data from your PS Vita system/PS TV system to your computer.
Like other Sony content management software, Content Manager Assistant is Windows-only. If you're a Mac user, you may have to either use your PS3 (if you have one) or buy a lot of memory cards (it may be possible to transfer files by connecting via USB and using Content Manager on the PS Vita itself.)