Short for "Touch My Gits".
You can probably guess what "Gits
" means, anyways.
This is similar to saying "Kiss My Ass", but only works for girls... or really whacked up sick-minded guys... or in the rare case, a genderless flying squirrel sub-species that depends on survival completely through asexual reproduction.
It can be used in a variety of different ways, to portray different emotional states or feelings.