When bidding on an item, you're actually setting a maximum bid (the UI does say that, but it's easy to miss; I know I did). The auction house will slowly increase your current bid as needed to keep you winning the auction, until you exceed your maximum bid.
When you place a bid, you'll get an entry in your Auctions tab that looks like
When I first bid on that item the displayed Bid was around 500. The auction house immediately made the current bid around 510, with me winning. As other people have come in and placed bids, my current bid has increased to exceed their maximum bids.
If you win an auction you get both the item and the gold difference between your maximum bid (which you ponied up in full when you placed it) and the current bid when the auction ended (less transaction fees, naturally). Hypothetically, if that auction were to end right now I'd get back about 18k in gold and the Champion Apex.
Blizzard explains the process here:
[T]he system will automatically place a bid at the lowest possible
winning price, in 5% increments (but no lower than 10 gold / $0.10 USD
or equivalent), up to the maximum the player sets.
It's not clear to me what that 5% is a percentage of, but I suspect it's the Current Bid.
Note that your maximum bid is not visible to other people. While it could be determined by placing bids incrementally higher bids, this is so tedious as to render it basically untenable.
As a complete aside, the complexity of the commodity and bidding portions of the auction house is sort of impressive. It makes the recent outages more understandable, if still really really frustrating.