My MWs have done this three times now, and while it's not the most comfortable thing in the world, it's not the worst, either. I think more than actually stripping the membranes they're really just stimulating my cervix, but that's neither here nor there.
Anyways, A membrane sweep (or strip) is when, during a vaginal exam, the examiner inserts his or her fingers into the cervix, and sweeps their finger around, separating the bag of waters from the cervix. This releases prostiglandins and sometimes is enough to get things moving. Obviously, if your body isn't ready, it's not going to do much. After my three sweeps I've had contractions and cramping for a while, but then they peter out.
Sex, IMO, is a better way of stimulating the cervix, and there are prostiglandins in semen that help with ripening. Inserting EPO vaginally (my mws have been rubbing it on my cervix) is another great way of encouraging your body to get moving.
FWIW, I'm 42w1d today, and I refuse to talk induction. I had a NST on Monday and a BPP today, and we'll repeat that next week, but as long as I'm fine and the baby's fine, I'm waiting. That may not be your cup of tea, but for me, it's better than pit.
Good luck!