A premise in debate or logic means the proposition from which a conclusion is drawn. The proposition (the premise) can be either proved or supposed. It is needed in order to apply logic and draw the desired conclusion.
A common flaw in reasoning is to apply correct logic to a faulty premise, as in "if embryonic stem cell research will save lives, then we should support it!" The premise of embryonic stem cell research saving lives is unproven and unjustified as a supposition, as all research has shown it to be essentially worthless. Note that statements of this sort ("if A, then B") require a correct premise, since no conclusions can be drawn from a false one - only propositions that take the more exclusive form of "only if A, then B" directly couple the truth value of the consequent to that of the antecedent in order to present a dichotomous choice.
The term the premises also has a legal and popular meaning, to include both land and buildings together as property, as in "he was on the premises at the time."