What it is
Three pieces: a bowl, a lid and a saucer. Leaves go in the bowl, water goes on top, and the lid is tilted to hold the leaf back while you pour the liquid off. There is no infuser and no filter of any kind. It is the simplest possible brewing device and takes about ten minutes of practice before it stops being awkward and about two weeks before it becomes faster than anything else.
What it is for
Many short infusions of the same leaf rather than one long one. A gaiwan holds little enough that a full one is a couple of small cups, so you brew for seconds rather than minutes and go again. The point is that the tea changes across those infusions — an oolong may take eight or more and be noticeably different at the third and the seventh — and a mug cannot show you that because it is all over in one go.
Whether you need one
If you drink a large mug at your desk and want it to taste good, no, and nothing here will change that. If you want to know what a rolled oolong or a good puerh actually does over time, yes, and it is inexpensive — porcelain gaiwans are among the cheapest brewing vessels made. The two are different activities and neither is the serious one.
Practical notes
Porcelain is the default and is neutral. Thin rims get hot; a slightly flared rim is much easier to hold. Fill it under the rim rather than to it. And pour it out completely every time — leaf sitting in residual water is the main reason a gaiwan session goes bitter by the fourth steep.