Comma splices are a type of run-on sentence in which two independent clauses are joined with a comma and made into one incorrect sentence.  Each phrase can stand on its own as a sentence because each has a subject and verb.
For example:
We watched TV tonight, it was good.
OR
I didn't know what job I wanted, I was too confused to decide.

You can fix these problems three ways.
First of all, you can split the halves of the sentences into two separate sentences.
For example:
We watched TV tonight. It was good.
OR
I didn't know what job I wanted.  I was too confused to decide.

The second way to fix a comma splice is to add in a coordinating conjunction, or a connecting word.  Some common connecting words include "and," "but," "yet," "or," "nor," "so."
For example:
We watched TV tonight, and it was good.
OR
I knew what job I wanted, but I was too confused to decide.

The third option is to join the two phrases with a semicolon or with a semicolon and certain specific connecting words like "however" or "yet," followed by a comma.  Just a semicolon is best if the two halves of the sentence agree with each other.
For example:
We watched TV tonight; it was good.
The semicolon and the connecting word is most often used when the two phrases present a contrast.
For example:
I knew what job I wanted; however, I was too confused to decide.

To spot comma splices: Watch for phrases with a subject and a verb that could stand on their own as a complete sentence.