Vita:Partitions and Mountpoints
The Vita, like its predecessor, uses a DOS-like drive management where different partitions get their own drive "letters" and don't share a common root.
NAND
os0
This partition contains the core operating system (kernel, modules, and boot script): any console can theoretically boot safe mode as long as os0 and the preceding binary blobs on the eMMC (partition table, bootloader, idstorage) are in good condition.
vs0
Contains the LiveArea and most of the stock applications.
vd0
System configuration.
tm0
Licensing data (PSN account activation, etc)
ur0
General application data for system titles, including the application/media database.
ud0
Usually an empty filesystem, used for storing the installer and package of an in-progress update.
sa0
Additional static system data that is rarely changed, such as predictive text dictionaries, separated from vs0 to allow it to be distributed separately therefore reducing the average update size.
pd0
That multi-minute intro video and Welcome Park - conveniently, all optional for the operation of the system.
ux0/imc0
This partition is only present on Vita 2000 and PSTV systems (although any console can be repartitioned to have it using Vita:IMCUnlock or equivalents).
It is normally mounted as ux0 if no memory card is inserted, or not at all if one is; StorageMgr suggests assigning it imc0, which is officially defined but not generally used (except possibly for the data transfer feature?).
Memory Card
ux0/xmc0
Applications, their update packs and DLCs, their data (saves), media files...
Like the internal storage equivalent, this also has a fixed name of xmc0, but in official practice is only ordinarily accessed as ux0, substituting itself to the internal partition if it exists.
Game Card
gro0
The title(s) distributed on the card.
grw0
A writable partition for saves, present on only a few releases.
USB device
See also: PSVSD
The PSTV can officially mount USB storage devices (more specifically, the first MBR partition or the entire block device, formatted as FAT32 or exFAT) as uma0, albeit only when loading updates off it.
SD Card
Developer Vitas have a real SD slot, which is mounted as sd0.