Run-on sentences contain two or more independent clauses that are joined incorrectly without proper punctuation or conjunctions. To correct run-on sentences, the clauses can be separated with punctuation like periods, commas, or semicolons. Conjunctions like "and", "but", or "because" can also join the clauses. Rearranging or rewriting the sentence is another option to avoid run-ons. The document provides examples of run-on sentences and their corrected versions.