A run-on sentence happens when a semicolon is omitted between two independent clauses not joined by a coordinating or correlative conjunction. Sometimes a comma might appear, but that's incorrect punctuation. To join two independent clauses without a conjunction, you must use a semicolon, as in John played the guitar; Mary sang the melody.
You can fix run-on sentences by (1) adding a semicolon, (2) breaking the run-on sentence into two sentences, (3) using a conjunctive adverb with a preceding semicolon and trailing comma, or (4) using a coordinating conjunction.
Here are some examples of run-on sentences, with fixes shown parenthetically):
It was late, we went home. (It was late; we went home.) (It was late; therefore, we went home.)
The research was defective, the partners were upset. (The research was defective; the partners were upset.) (The research was defective. The partners were upset.) (The research was defective, so the partners were upset.)