Semicolons are used to separate independent clauses in three different cases.
1. When there are no conjunctions separating the clauses.
Incorrect: I like you, John likes you, too.
Correct: I like you; John likes you, too.
2. When the clauses are separated by a conjunctive adverb or other parenthetical expression set off by commas.
Correct: I am crucified with Christ; nevertheless, I live.--Galatians 2:20.
(Nevertheless is a conjunctive adverb.)
Correct: Hector was a Trojan; Achilles, on the other hand, was an Achaean.
3. When the clauses themselves contain commas.
Incorrect: He wears shoes with kilties, a leather fringe, but I prefer penny loafers myself.
(Since clause already has comma, semicolon separating the clauses is needed to make sentence clear.)
Correct: He wears shoes with kilties, a leather fringe; but I prefer penny loafers myself.