Veteran status is a rank achieved in different games. It allows a bonus in combat ability. It can be gained by victory in combat.
Some games rank advances to be done by other means as well.
In Sid Meier's Alpha Centauri, there are base facilities that can be built to upgrade units, as well as Secret projects. You can also upgrade a unit one rank above what it currently is, by moving it to where a monolith is located.