They've is a contraction that combines two words: “they” and “have.” When you write they've, you're simply shortening “they have” by replacing the “ha” in “have” with an apostrophe.

You'll see this contraction everywhere in everyday writing and speech. Someone might say they've finished their homework, meaning they have finished it. Or you might read that scientists have discovered something new: they've found a fossil, they've solved a puzzle, they've tested a theory.

Contractions like they've make language flow more naturally. Compare “they have been working hard” to they've been working hard. The second version sounds more like how people actually talk. In formal writing, like a research paper or business letter, you might spell out “they have” instead of using the contraction, but in most everyday situations, they've works perfectly well.

One common mistake: don't confuse they've with “their” (which shows possession) or “there” (which refers to a place). If you can replace the word with “they have” in your sentence, then they've is correct.