PSP
PSP stands for PlayStation Portable, a portable video gaming and entertainment device manufactured by Sony. Anyone who uses one could be considered a "PSP user." Sony has contracted with several video game developers to produce titles for this system. Additionally, it plays movies on small discs called UMDs, which are often for sale wherever you can buy PSP games. The PSP can save data to Memory Stick Duo units, on which users can also store photos and music that can be viewed or played back on the PSP. These units can use Wi-Fi to browse the Web or visit Sony's online PlayStation Store and download additional games and other content from the site. This oldest member of Sony's portable gaming family is referred to as PSP-3000 on Sony's website, but is more commonly referred to simply as the PSP.
PSP Go
Other PSP users might use the PSP Go, which is a lightweight, streamlined version of the PSP. Unlike its predecessor, it lacks the ability to play disc-based PSP games or UMDs. Instead, users of this particular PSP must download games from the PlayStation Store using the system's built-in Wi-Fi connection. It also has a smaller screen than the original PSP, but features 16GB of built-in memory, which is an upgrade over the PSP. It supports the Memory Stick Micro for removable memory, as opposed to the Memory Stick Duo supported by the original PSP.
PS Vita
On June 6, 2011, Sony announced the name of the successor to both the PSP and PSP Go systems: the PS Vita. Whether or not its name will be shortened to an acronym, such as PSV, remains to be seen. This next-gen portable gaming system features several improvements over its predecessors, and will probably attract a fair number of current PSP users.
Considerations
Being a PSP user doesn't exclude other types of video gaming. Depending on your wants and needs, you can concurrently be a Nintendo DS user, PS3 user, Xbox 360 user or any other type of gamer you prefer. When the PS Vita is released, you may even be a PSP user and a PS Vita user as well. Furthermore, being a user of the system doesn't necessarily mean you have to own it. If your sister loans you her PSP, and you use it, you're a PSP user as well -- at least, while you're using it.