A RUN-ON SENTENCE (sometimes called a "fused sentence") has at least two parts, either one of which can stand by itself (in other words, two independent clauses), but the two parts have been smooshed together instead of being properly connected. Review, also, the section which describes Things That Can Happen Between Two Independent Clauses.
It is important to realize that the length of a sentence really has nothing to do with whether a sentence is a run-on or not; being a run-on is a structural flaw that can plague even a very short sentence:
The sun is high, put on some sunblock.
An extremely long sentence, on the other hand, might be a "run-off-at-the-mouth" sentence, but it can be otherwise sound, structurally. Click here to see a 239-word sentence that is a perfectly fine sentence (structurally)
When two independent clauses are connected by only a comma, they constitute a run-on sentence that is called a comma-splice. The example just above (about the sunscreen) is a comma-splice. When you use a comma to connect two independent clauses, it must be accompanied by a little conjunction (and, but, for, nor, yet, or, so).
The sun is high, so put on some sunscreen.
Read more at the links provided above.