What exactly is a menstrual cramp? is it just soreness from the uterine lining sloughing off, or does it actually have to do with muscle contraction?

Contraction: Chemicals called prostaglandins are released that lead to the uterine muscle contractions and other unpleasant symptoms during your period.

Uterus contraction: The inside lining of your uterus grows in response to female hormones, and sloughs during a period releasing hormones called prostaglandins. They make your muscular uterine walls contract. Drugs like Ibuprofen & Naproxen block production and reduce pain; best taken at the earliest onset of cramps. Also birth control pills reduce growth of the lining, hence reducing cramps too.