Makes the SLR camera look wayyy coooler, and as a side-effect makes the person holding it look more professional too.
It's main purpose is for ergonomics. Instead of twisting your arms and showing off your armpit hair in the process of taking a portrait-oriented shot, with the vertical grip you just turn the camera 90 degrees.
It also acts as a battery pack that accepts a 2nd (set of) battery, and thus extends the number of shots between battery charges.
It is an accessory for most D/SLRs that accept it, and often every D/SLR model will have it's own specialised vertical grip. Often, a vertical grip help balances the weight of a small SLR when mounted with big lenses.