A run-on sentence is a sentence that joins together two ideas together improperly. You'll know it's a run-on sentence if it's either really confusing or it has lots of commas without conjunctions.

Example of a run-on sentence:
I had to run to school Jimmy did also.

That makes me cringe. It's awful looking, sounding, and it's just a plain ugly sentence. There are two types of run-on sentences: fused sentences and comma splices.

Fused sentence -- when two ideas are joined together without any conjunctions or commas in between them. The example above was an example of a fused sentence.

Comma Splice -- the use of a comma to join two ideas without a conjunction.

An example of a comma splice:
He walked to school, Jimmy did also.

That also makes me cringe.

The way to fix run-on sentences, because of course we want to fix is by adding either a comma and a conjunction or by just adding a conjunction. A conjunction is a word that joins two clauses or thoughts together. I'll get into the different types of conjunctions later, but for right now let's focus on a set of conjunctions that can be abbreviated to the word FANBOYS (coordinating conjunctions).

F--for
A--and
N--nor
B--but
O--or
Y--yet
S--so

You use those along with a comma to fix a run-on sentence. Let's go back to the previous one:

Original: He walked to school Jimmy did also.
Correct: He walked to school, and Jimmy did also.

See all good. Now, run-on sentences come more naturally when you're texting or when you're writing through a character that speaks that way, but they're incorrect. Fused sentences are especially confusing and comma splices just kinda . . . look wrong to me.

Commas save lives!:

Let's eat grandma!

Let's eat, grandma!

You're actually supposed to put a comma before the name if you're addressing someone at the end of the sentence. If you don't, the person you're addressing turns into the object which means that it's being acted on.

Remember, don't eat your grandma.