Membrane sweeps are sort of the "most invasive" of the natural induction methods and the "least invasive" of the medical methods. The basic idea is to lift the bag of waters off the cervix (this causes a shift in hormones) while manually dilating the cervix itself (similar to what a foley cath would do, but on a much smaller scale). The hope is that with the hormone surge and the more open cervix, the body will take over and labor will begin. Some care providers will put EPO, Borage Oil, or other natural induction aid on their fingers, working it into the cervix as an extra whammie. And while some providers will do a membrane strip/sweep and take only a minutes or two, others feel that to be effective the sweep needs to take 10-15 minutes at least. It's essentially a really really intense vaginal exam/pap smear sort of experience. So not something you'd do for fun, but not something that is off the charts painful for most women. I usually think of it as a good time to practice labor coping techniques. lol
Risks include breaking the bag of waters, infection (especially if you have GBS), and cervical swelling. Benefits include the chance of staring labor without chemical induction methods or AROM (with the "clock" that often comes along with AROM). Some women find it very uncomfortable or even painful, others barely notice it. Some women find that they start contracting or have spotting/bloody show more or less immediately while others feel just a little crampy and that's it.
With my first pregnancy I had 3 membrane sweeps (40 weeks, 41 weeks, 42 weeks) and while they were uncomfortable they weren't painful, and they certainly didn't do anything to start labor since dd1 was born a few days past 42 weeks. With my second pregnancy/first vbac I again had several membrane sweeps... again they weren't terribly uncomfortable, and I don't know what role they may have played in starting labor, though dd2 was born within 24 hours of a sweep and she was my "earliest" babe at just over 40 weeks. With my third pregnancy/second vbac I again agreed to having my membranes swept. The first time at 39 weeks, then 40 weeks, and finally at 41 weeks. The 41 week sweep was my first "dear gods painful" sweep and it was with a midwife who fell into the "long slow sweep" category. I did deliver about 12 hours after that sweep.
So... I never had any real complications, only once was it actually painful rather than uncomfortable, but I can't really say it did much. I do plan on asking for a sweep at my next visit (39 weeks) however. I think that it's one of those things where the risk/benefit balance is going to be very personal. If you're dealing with a deadline of sorts (like many vbac moms) or have a complication that might become acute in later pregnancy (blood pressure concerns or something similar) then it makes more sense to try a sweep. But if you don't have any "reason" for trying it, the risks might outweigh the benefits.