A run on sentence is any sentence that contains multiple, unrelated clauses. An example:

We cooked the food over the campfire and had to pitch the tent under the tree.

Technically, this has two ideas in one sentence that are functionally unrelated. In our example, the clauses are topically related (camping), but have no relation to one another (spatially, temporally, etc.)

You can rectify a run-on in a few different ways, depending on the circumstances. We can fix the problem by relating the two concepts, if appropriate. An example of a related, and therefore, non-run-on sentence:

We cooked the food over the campfire while pitching the tent under the tree.

Now the clauses are interacting.

You can also always break the sentence into smaller sentences to resolve the problem.

We cooked the food over the campfire. We had to pitch the tent under the tree.

Use of a semi-colon or comma is sometimes appropriate as well. Here's an example:

We ran the race in two hours and didn't place in the top three.
BECOMES
We ran the race in two hours; we didn't place in the top three.
OR
We ran the race in two hours, but didn't place in the top three.

Notice how the semi-colon or conjunctions signals a relationship between the two clauses. Otherwise the ideas the sentence is trying to express would not be hurt by breaking up into two sentences. In other words, a single sentence is only, but not necessarily, appropriate when the two concepts must relate to one another.