A "run-on" or fused sentence occurs when the writer has blended two or more complete sentences into one without using enough punctuation: a semi-colon, or a comma with a linking word (and, but, for, nor, so, yet). Run-on sentences are typically compound sentences without the proper punctuation and/or linking word.
Here's an example of a run-on sentence:
Leonardo DaVinci was a great painter, he was also an inventor.
Here is how you can fix this run-on sentence:
Leonardo DaVinci was a great painter. He was also an inventor.
Leonardo DaVinci was a great painter; he was also an inventor.
Leonardo DaVinci was a great painter, and he was also an inventor.
As you can see, a comma is not strong enough to hold these two complete thoughts together. In fact, two complete sentences linked only with a comma and lacking a linking word are sometimes called a "comma splice," which is a type of run-on sentence error.
To fix run-on sentences:
Place a period between the two complete thoughts.
Place a semi-colon between the two complete thoughts.
Place a comma and a linking word between the two complete thoughts.