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If there are several sentences that have a coordinate conjunction between them — usually this is the word “and” — it is correct to put a comma before the coordinate conjunction, the “and.” There seems to be some discussion that, when there is a string of these sentences, there is no need for the commas. I know of no such rule.
This is often called a “narrative,” which features several sentences strung together with “and.”
After two or three sentences like this, it is best to use a period and start the next sentence with “and.” And after six or eight lines, there should be a paragraph, which, yes, begins with “and.”