The phrase "God Damnit", which when expressed in a grammatically correct fashion would read "God Damn It," is a vulgarity used to express frustration. It's literal definition is "May the Christian God Damn it to Hell". In slang, it is a phrase used in a generally non-religious context. For example, if one cannot get an electronic device to work properly, one might exclaim "God Damnit!", meaning that you are so upset with the device you wish that God would condemn it to eternal damnation.
It is rarely used literally, and is considered a lesser of vulgarities, though to the extremely religious it is considered highly offensive. In the Christian faith it is considered a violation of one of the ten commandments.
"I can't get this VCR to work! God Damnit!"