There are two uses of semicolons in English. This entry will deal with the more common use.

Use a semicolon to join two independent clauses, meaning two clauses that can each stand alone as a sentence.

Examples:
John loves to sell houses; he’s a real estate agent by trade.
Frank dislikes selling houses; nevertheless, she’s a real estate agent by trade.

The semicolon often seems to lend an air of formality to a sentence. Both examples could have been broken into two sentences for a slightly more casual feel (although it’s hard making a word such as neverthelesssound casual). The semicolon also makes the relationship between ideas seem closer than a period would.