A run-on sentence occurs when two or more sentences are joined incorrectly.
You should be able to spot run-on sentences with your eyes closed—if we read them out loud to you, that is. Run-ons are not just long sentences. We repeat: long sentences are not a crime against the Grammar Overlords.
Run-ons, however, are basically punishable by death.
There are two types of run-on to put on your radar so you can avoid them like the plague. (Shmoop PSA: to avoid the plague, do not lick any rodents that are acting sickly or erratic.)