A vote of confidence is giving someone one your support. It can be an actual formal vote of confidence or no confidence, usually when someone is screwing up their job; or it's just an informal "Heh, you have my vote of confidence! I know you'll do a good job."
When I was a pledge the Panhellenic Council on campus took a vote regarding a struggling chapter. They voted no confidence in the chapter because it was struggling so very badly. Their National Council shut them down within the week. Coincidence? I don't know...
