What's a run-on sentence?
A run-on sentence occurs when two or more sentences are joined together without appropriate conjunctions or punctuation.
Compound sentences should contain independent clauses that are closely related to each other. Coordinating conjunctions must be used to join related independent clauses. If the clauses are very closely related, it is possible to leave out the conjunction and put a semicolon in its place. When a writer tries to join sentences with just a comma, it is called a comma splice error.
Examples
1. Harriet Tubman was a slave who escaped to the North where she worked and saved money, she went back to the South even though she risked arrest and helped her sister’s family to escape.
Harriet Tubman was a slave who escaped to the North where she worked and saved money is a complete sentence.
She went back to the South even though she risked arrest and helped her sister’s family to escape is another complete sentence. Therefore, it should be separated from the first sentence. You could correct this by making it into its own sentence, by capitalizing the "S" in "She" and placing a period at the end. You could also keep the two clauses as one sentence and separate them by a semicolon, since they are closely related.
2. Tubman behaved heroically, many people still do not know about her.
Tubman behaved heroically is a complete sentence. Many people still do not know about her is another. In this case, the writer has an opportunity not only to correct the comma splice error, but to make the meaning of both sentences clearer. The second sentence provides information that contrasts with that in the first sentence. The comma splice does not convey this relationship; but simply dividing the sentence into two, while it's grammatically correct, does not improve matters sufficiently.
A better way to revise this sentence would be as follows:
Tubman behaved heroically, but many people still do not know about her.
The coordinating conjunction but joins the clauses in a grammatically correct manner; moreover, but adds information to the new sentence to make its meaning clearer.