I didn't read the other responses so it wouldn't influence my post.

I think "Trusting birth" means to me that you believe in birth - in babies - in mothers - in the process and in creation (however you phrase that) to do it perfectly. I think that it is rare that given information, space, confidence, choices and trust, that a Mom and baby don't work birth out on their own.
If someone does not trust themselves they will not hear the inner voice telling them to take a particular positon to birth or labor. They will look to someone else to tell them what to do, to manage things (I know that isn't all the time - every rule has an exception, but speaking in somewhat generalizations here).
I think first believing in yourself is the foundation to believing in birth. If you think, "Gee, what a MIRACLE it is that this baby grew to this perfectly made little being in there, ready for birth, ready for life. My body and my baby DID that! I am a part of an amazing thing!", then it's likely that you can also think along the same lines that IF your body did that, it is possible that indeed it can ALSO birth that baby!
If you go into it thinking "Well my provider is monitoring my baby so it doesn't get too big and is thinking that it would be easier to have me go in for an induction at 38w because they will be on vacation starting that Friday" you have given away your choices and empowerment to someone else and forfeited the confidence. Sometimes babies are 'too big' but there is aparantly an epidemic that only induction will save us from (big time joking) - so the delicate balance is already nuts here. Does she know the truth of pregnancy and birth? I would guess no.
So this could turn into a huge detail-induced post - but that's what it means to me. I think trusting birth has to be on both sides of the coin (provider and Mom) to work well. It can work otherwise, but to work well...
Honestly, sometimes I feel that who cares about body-image, I'm after birth-image!

It's all tied together...