No, doulas have no medical training, although some are trained to perform cervical exams. They are not medical professionals.
You can also visit alace.org for some more info.
A doula helps mom with position changes, "therapeutic touch" (not a massage per se, since not a LMT), encouragement, relaxation, aromatherapy, foot rubs, counter pressure, getting and fixing snacks and drink for mom and dad, etc.
In a medical setting (ie hospital) where the midwife may be attending several births, as well as charting, seeing pts on the ante partum floor and the clinic, a doula can be most beneficial because she is there the whole time-with ONLY that woman.
They are also very helpful at homebirths, as an above poster mentioned. Many home birth doulas arrive to help the mother well before the midwife needs to be there.
Big difference in the pay as well. As a doula, I make between $0-$700 per birth (though only made that $700 once, and worked my butt off for it too!). I also volunteer a lot, which explains the zero.
But we're both on call, and both there for the same reason--to help mom and baby have the safest, happiest, easiest delivery possible.