A run-on sentence does just what its name says it does: it runs on and on and on and by the end of it you are out of breath just like you would be if you were running for a very long time without stopping for a break even if you needed some water or something you could not stop so no wonder you are tired and confused and panting by the end of it that is what a run on sentence is oh god when will it stop.
What is it?
A run-on sentence occurs when a writer joins two (or more) independent clauses together without punctuation. As you saw, a comma splice joins two independent sentences together with a comma. Well, a run-on does it with no punctuation at all.
Why is it incorrect?
Two independent clauses cannot stick without anything there to hold them together.
What does it look like?
It’s cold out there you should wear a tuque.
How can you fix it?
1) Add a period: It’s cold out there. You should wear a tuque.
2) Add a semicolon: It’s cold out there; you should wear a tuque.
3) Add a conjunction and a comma: It’s cold out there, so you should wear a tuque.
4) Avoid the urge to just add a comma. This might feel good, but it will only result in a comma splice.