This dimension used to be called visit count, session count is the session index of a user. Every session created by a unique user will get its own incremental index starting from 1 for the initial session. Further sessions do not change the previous session indices. Session count can be used within segments in your Google Analytics platform, it is written in queries as:

ga:sessionCount

Example

A user has 6 sessions on your website, the session count for that user will have six separate values of 1 through 6.