Theory?
"In as few words as possible: What exactly is the "Lifeboat Mars" theory?"
Not a theory, barely qualifies as an idea- more like a slogan. The correct wording is "don't have your eggs in same basket"- the end of the world type ideas have always had broad public appeal. The idea is that people could be living on Mars, and if everyone dies on Earth then there would still be humans living on Mars, hence human species would not become extinct.
It's fairly ironic since NASA has been putting most of it's eggs in the Mars basket. Their fervent hope is that the tax payers will do another Apollo program- this time with Mars.
Since you want only a few words, I'll leave it at that.
-gb