Technically, System V is the name of a UNIX system produced by AT & T. It was (unsurprisingly) the successor to System IV. It is often used to describe a family of UNIX systems, to differentiate them from BSD systems. In particular, there are several system facilities that are quite different on BSD and System V. For example people refer to "System V init" or "BSD init". The former organises scripts for starting and stopping services into a directory for each runlevel, the latter has a single script for each runlevel.
In many cases Linux has features from both families of UNIX. The program ps, for example can support both BSD and System V commandline options and it is possible to use whichever style of init one chooses, although most distributions use Sys V init.