If Bigfoot walked down your street wearing a tutu, you might gape or stare at the man-ape with your mouth open. You'd really gape if the tutu had a gaping, or wide open, hole.
Gape is closely related to the word, gap, which means a space between things. When you gape at something, there is a lot of space between your teeth because your mouth is open in disbelief. You'll often hear mothers telling children not to gape. The fact is it's rude to stare at someone that way, even if they are a Sasquatch on the way to dance class.