Semicolons are like perfume; used correctly and in proper measure, they’re sophisticated and add richness. If you use them incorrectly and too often, they’re smelly and offensive.
Semicolons do not do the same things commas do. Commas separate clauses; semicolons separate sentences.
Notice the very helpful alliteration:
(Side note: a clause is a string of words that contains both a subject and a verb. Okay, back to semicolons.)
Sometimes, two complete sentences are very closely-related; sometimes they are so closely-related that they shouldn’t be divided by a complete end-stop, and you don’t want to separate them with a comma and conjunction.
Look at the sentence above; it serves as an example of many non-period punctuation options. “Sometimes, two complete sentences are very closely-related” is a complete sentence that stands on its own correctly, and so is “sometimes they are so closely-related that they shouldn’t be divided by a complete end-stop,” and so is “you don’t want to separate them with a comma and conjunction.” All three could be correctly separated by periods, making them three distinct sentences. It’s a matter of style. For example, “You don’t want to separate them with a comma and conjunction,” is technically a correct sentence, but it’s a bit awkward on its own. In my opinion, it “flows” better when it’s attached to the previous sentence with “, and.”
When your sentence contains a list, and each item on the list contains commas or a series of items within itself, semicolons are also useful and correct.
More on style and choice:
When you’re writing a scene, the punctuation choices you make are not arbitrary and do not always rely on what is “correct,” but those choices can accentuate what’s happening in the scene by affecting its pace.
If you’re going for an urgent, staccato effect, short, clipped sentences with few commas are appropriate. They add immediacy. Sometimes a well-executed sentence fragment works to its advantage.
When something more pensive or emotional is happening, you might not want to break the stream of language with a full stop, but writing “and” too much is cluttering the language. In this case, semicolons are very useful.
Now that you know how to use them properly, use them in moderation.