Think of two sentences that go together like peanut butter and jelly; each one is a separate thing, but wedded into a delicious sandwich. Examples? You mean, besides this one?
1. When zombies overran the town, we climbed up the mountain; we climbed as fast as we could.
(Here, you see, the object is to speed up the scene, to make the reader feel a sense of urgency. A complete stop just won’t do.)
2. We must work hard; we must work fast.
Note: A comma can be used in short sentence like #2, without the writer looking like a complete idiot, as in: Man proposes, God disposes. If you type Man proposes, God disposes on your word processor, you will see that it puts that wiggly green line under it, telling you that it’s not correct. Aha, this is where you become smarter than the program.
You might be especially interested in using a semicolon, when your sentence already has a lot of compounds in it, as in these:
3. She was beautiful and seductive; she was evil and undead.
4. The boat was made of steel and riveted bolts; still, I trembled before it like an overly large child and wept into my hands.
Note: Adding an adverb before the second part does not preclude a semicolon, as in:
5. You are a vampire; therefore, I can’t meet you at midnight.
6. I wanted to see the steely stud again; besides, I hadn’t been out of the house for a long time.
When NOT to use the semicolon: Your sentence must jive. Here an example of an error:
7. I like peanut butter and jelly sandwiches; I like my cat better.
(Now that’s funny. Sounds like you like to eat your cat. Wahahah!)