Meaning of Obey and Submit
John Piper is the best. I listened to a couple sermons by him on Monday that were preached on Hebrews 13:17, "Obey your leaders and submit to them, for they keep watch over your souls as those who will give an account. Let them do this with joy and not with grief, for this would be unprofitable for you." They were very good and in the second one when he talks about what obey and submit actually means, he takes a while to develop biblically and practically that leaders/elders can be very fallible and there needs to be safeguards in place.
Then at the end he asks:
What then does "Obey your leaders and submit to them" mean? The word for "obey" (peith) is a very broad word and means "be persuaded by" (Hebrews 6:9), "trust" (Hebrews 2:13), "rely on" (Luke 11:22), and comes to mean "obey" because that is what you do when you trust somebody. So you might say it is a "soft" word for obey. It encourages a good relationship of trust, but still calls for the people to be swayed by leaders.
The word for "submit" (hupeik) occurs only here in the New Testament. It's the more narrow word, and means "make room for by retiring from a seat," or "yield to" or "submit to."
So with all this background, what I would try to distill as the meaning would be something like this: Hebrews 13:17 means that a church should have a bent toward trusting its leaders; you should have a disposition to be supportive in your attitudes and actions toward their goals and directions; you should want to imitate their faith; and you should have a happy inclination to comply with their instructions.