The Utah Teapot is a sexual maneuver requiring three people - one man, and two women (one with a strap-on). It combines pegging and the teapot maneuver - the three people are in a line, facing the same direction.
The man is in the center, the woman wearing the strap on is in the back, pegging the man, with her hands on his shoulders, and the woman without a strap-on is in front, in the doggystyle position. Due to the orientation of those involved, the overall shape resembles that of a teapot - the woman in the front being the 'spout', the woman in the back being the 'handle', and the man being the body of the teapot.
The "Utah" correlation comes from the fact that two women and one man are required - a reference to polygamy/Mormonism/Utah.
I walked in on Dallin and his two wives, Jessica and Linda, doing the Utah Teapot the other night after temple. I then went and didn't have a drink, since it is forbidden in my faith.