This term is generally used to refer to military units that are part of the regular forces (not militia or reserve). For example, the US 101st Airborne Division is a regular unit, while the 1st US Army (Reserve) is not.

It can also mean a regular browser of a forum or website, such this one.

Also, in topology, a regular space is one in which points are closed and any point can be separated from any closed set by open sets.