Punctuation helps a reader understand your story. Commas, periods, dashes and other marks convey the writer's voice. They signal an emphasis or tone in language, as well as telling a reader when to stop or pause.
Think of punctuation this way: The comma is a slight break in the thought of a sentence; the semicolon is a longer pause; and the dash represents an abrupt, dramatic turn.
Semicolons are used to indicate a greater separation of thought and information than a comma can indicate (for example, in the previous paragraph). Here are some other examples.