Terse means brief, or using very few words. If your teacher tells you to make your writing in your essay style terse and to the point, he's saying use as few words as you can and be simple and clear.
A terse reply or command may seem rude or unfriendly—but the word terse itself doesn't mean unfriendly or rude. Synonyms are succinct or concise, though these words have a more positive tone. The adjective terse is from Latin tersus "clean, neat," from tergere "to rub off, wipe, polish." Polished language is neatly concise.