Sorry, I knew I forgot something.
There are two types of doulas: labor and postpartum doulas.
Labor doulas work with the mom before and during labor formulating and carrying out birth plans, doing non-pharmacologic comfort measures (massage, accupressure, position changes, emotional support, etc.). They are also very useful supporting the dad - since we are there, dad is more free to take a snooze, go for a snack, take a breather. In my hospital, we are allowed to go back for c-sections with the father. He sits down with the mom and I stand behind him. I can tell him what's going on with the surgery, when the doc has the head out, baby out, etc. When the dad leaves to take the baby to the nursery, I stay with mom and comfort her during the rest of the surgery. We can also help initiate breastfeeding, if necessary.
A postpartum doula focuses on what can be done for the mom after the birth. She is trained in basic mother/baby care, can do light housework, meal preparation, help with the other kids. This is especially helpful for the mom who has had a c-section, but is also helpful for those who've delivered vaginally as well.
Both are certified by such organizations as Doulas of North America and CAPPA.
Above all, doulas have their own job which is very different from the nurses. We do NOT interfere with their job. We can give suggestions, but we don't do any medical procedures for the mom (vag checks, bp checks, heart tone checks - however, at our hospital we can unplug/plug monitors if mom wants to go for a walk). The medical procedures fall into the realm of the nurse. We provide non-pharmacologic support, and try to follow the requests of the birth plan if feasible. If parts of the birth plan can not be followed, we do not argue - things come up and may not be possible. We do have the goal of the nurse - do everything possible to ensure the result of a healthy mom and baby.
There's so much more that I could go into, but this should do for now.
Hopefully this will help to answer any questions.