Use a semicolon between independent clauses with no coordinating conjunction.

Mt. Everest is the highest mountain in the world; it is 29,028 feet high.

Use a semicolon to separate items in a series which contains commas, or between independent clauses with a coordinating conjunction when there are many other commas all around.

She has lived in Dallas, Texas; Reno, Nevada; and Salem, Oregon.

Oh, by the way, Nora, John will be late, possibly very late; but, don't worry about it; if he's hungry, he can pop something in the microwave.