1] The face made when eating a very sour item, such as Sour Patch Kids or Warheads, where the lips pucker and contort in an unusual manner
2] A similar face made when someone is angry, upset, or annoyed
Reality show housewife 1: I asked my son to take out the trash; you wouldn't believe the sourface he gave me when I said it!
Reality show housewife 2: I would have given you the sourface too! I just have our maid do it.
Reality show housewife 1: And that's why you're $80,000 in credit card debt and your house is in foreclosure
Reality show housewife 2: *Gives the sourface*
"You wouldn't believe my husband! I told him to go clean out the garage and he didn't, so I turned the TV off while the game was on, and he gave me the biggest sourface I've ever seen! Then he mumbled something about me getting back in the kitchen and making him a sandwich."