The rule of putting a period at the end of every thought would be simpler, except that in English, we’re allowed to include more than one thought in the same sentence. These thoughts are expressed in clauses, and clauses can be independent or subordinate. For example, that last sentence has two independent clauses, separated by a comma and the word and.
With independent clauses, both thoughts don’t have to be included in the same sentence. In the previous paragraph, I could have said, “These thoughts are expressed in clauses. They can be either independent or dependent.” Do you see how independent they really are? They make sense even when they’re separated.
Putting a period between two independent clauses usually doesn’t make them any harder to understand. The rhythm or flow of the writing is a little choppier, but that is it. Most of the time, long sentences are overused and short sentences are underused. Pay attention to your writing. Are you jamming multiple thoughts in one sentence? Are you doing that over and over again? Perhaps you should use the period more often!