It's no accident that a semicolon is a period atop a comma. Like commas, semicolons indicate an audible pause—slightly longer than a comma's, but short of a period's full stop.
Semicolons have other functions, too. But first, a caveat: avoid the common mistake of using a semicolon to replace a colon (see the "Colons" section).
Incorrect: I have one goal; to find her.
Correct: I have one goal: to find her.
Rule 1a. A semicolon can replace a period if the writer wishes to narrow the gap between two closely linked sentences.
Call me tomorrow; you can give me an answer then.
We have paid our dues; we expect all the privileges listed in the contract.
Rule 1b. Avoid a semicolon when a dependent clause comes before an independent clause.
Incorrect: Although they tried; they failed.
Correct: Although they tried, they failed.
Rule 2. Use a semicolon before such words and terms as namely, however, therefore, that is, i.e., for example, e.g., for instance, etc., when they introduce a complete sentence. It is also preferable to use a comma after these words and terms.
Example: Bring any two items; however, sleeping bags and tents are in short supply.
Rule 3. Use a semicolon to separate units of a series when one or more of the units contain commas.
Incorrect: The conference has people who have come from Moscow, Idaho, Springfield, California, Alamo, Tennessee, and other places as well.
Note that with only commas, that sentence is hopeless.
Correct: The conference has people who have come from Moscow, Idaho; Springfield, California; Alamo, Tennessee; and other places as well. (Note the final semicolon, rather than a comma, after Tennessee.)
Rule 4. A semicolon may be used between independent clauses joined by a connector, such as and, but, or, nor, etc., when one or more commas appear in the first clause.
Example: When I finish here, and I will soon, I'll be glad to help you; and that is a promise I will keep.
Rule 5. Do not capitalize ordinary words after a semicolon.
Incorrect: I am here; You are over there.
Correct: I am here; you are over there.