One of the reasons China periodically threatens Taiwan is to remind Chinese citizens that the Chinese government is powerful. It helps to prevent Tiananmen Square type incidents.

As other people have said though, China does not have a strong enough navy (by several orders of magnitude) to get an invasion force anywhere near Taiwan. Where do you think all those submarines that the US built during the cold war are right now? Enough of them are near Taiwan at any given time to make a sea-borne invasion impossible.

They could airdrop troops, or even just bomb the island, but there's no way they could bring enough combat power to actually hold it. Furthermore, knowing that the US can handle the water approaches, the Taiwanese government has spent its money build up air defenses. China can expect heavy, heavy aircraft losses if they try anything - and aircraft loses are very expensive.

They could try nuking Taiwan, but that would open up a whole new can of worms that they probably don't want to deal with. The only remaining military option would be a terrorist campaign, and like going nuclear, I don't really see what the point would be.