Here is the dictionary definition:
1 ancestor: someone from whom you are descended (but usually more remote than a grandparent)
2 a preceding occurrence or cause or event
3 anything that precedes something similar in time; "phrenology was an antecedent of modern neuroscience"
4 the referent of an anaphor; a phrase or clause that is referred to by an anaphoric pronoun
5 preceding in time or order
The word can also be used to describe the first half of a hypothetical proposition: if P than Q, the 'if P' part is the antecedent for the proposition. If hell freezes over, than Julie will sleep with me, "if hell freezes over' is the antecedent.