A super short version?
"Pre-millennial" means the belief that Christ will return before the 1000 year reign mentioned in The Revelation. But it's not this aspect that is so troubling.
"Dispensationalism" (perhaps an oversimplification:
1) God governs history through seven "dispensations" (periods of history) wherein the way to be right with him is different each time
2) the Jews have a separate destiny than the Gentiles; God deals primarily with the ethnically Jewish people, the time of the Gentiles is a parenthetic in their story
3) an over literal reading of apocalyptic texts (e.g., "the wasps in revelation are Huey model 4A"
It's not quite as prominent as it used to be, and has been modified quite a bit since the turn of the 20th century when it was dominant, but these inclinations linger.
Others please chime in if I've misrepresented or left something out, but thise three points are the essence of (classical) dispensationalism, as I understand it.
