Grammar #2

I have never clearly understood how to use the semi-colon. All I know is that when I have written different papers occasionally my grammar check tells me to add a semi-colon, which I automatically follow the instructions, but not really knowing why.
According to essortment.com (http://www.essortment.com/all/semicolon_rcnr.htm) there are two main ways to use a semicolon.
"The semicolon is a simple piece of punctuation, much easier to work with than the comma because it follows fairly clear rules. If you learn the two simple rules explained here, you'll rarely go wrong. It has two main uses, which are both easy to identify. You use it to connect two independent clauses together into one sentence, and you use it as a super-comma."

To Connect Two Independent Clauses

"Independent clauses are series of words that could stand alone as complete sentences. When you have two otherwise complete sentences that you want to connect to form one long sentence, use a semicolon."

To Serve as a Super-comma

"When you have a series of three or more items that normally would be separated by commas except that each individual item already has a comma in it, you use the semicolon between items."