Power
As the name implies, the midwife's generally in the middle of it all. You help the mother deal with the child, both before it comes and after it arrives. You assist the attending physician with general nursing duties, and you assist the birth by simply being a person the family can trust.
Depending on the situation, you might even be delivering the baby yourself. Everybody needs you there—but they don't necessarily want you to tell them what to do.
Obviously, there's a lot of helping and generally just being there in your job. You mostly do what other people—the physicians, the hospital managers, the stressed-out parents, the tiny human about to dive into this world—tell you to do. If the expectant mother wants a pool birth and hospital facilities allow, you give them a pool birth.
If she wants a natural birth, you give them a natural birth. If she wants the child born inside the cockpit of a fighter jet, you strap in and take your motion sickness pills.
Besides the birth itself—where you take on whatever role's required of you and you say thank you—in your day-to-day you'll generally have the typical power of a medical professional. You can write prescriptions, meet with patients, and act as an active assistant to the birthing process, from pregnancy to delivery and beyond (source).
We wouldn't call you a co-birther, but you're definitely a member of the birth committee here.