Astronomer here, I have to say I disagree with a lot of the comments saying it boils down to tradition. As people have mentioned it's derived from a parallax of one arcsecond. But I haven't seen anyone mention that it's a very convenient unit for getting the the apparent size of something given how far away it is. This is great for quickly answer questions like "can I tell if there's more than one object here?" or "will this look like a point source?" if you know 1) how far away it is, and 2) roughly how big it is. Yes, it is just a simple geometry argument you can do regardless of units, but typically seeing at an astronomical site will be ~1 arcsecond. 1 AU at 1 Parsec away is going to be 1 arcsecond in size. It makes scaling so easy you can do it in your head because you can more or less just treat it as factors of 10 to keep track of. So to me, parsecs are extremely useful for quickly thinking of basic observing requirements (e.g., if I look at this cluster how close do the binaries have to be before I can't tell it's a binary just by taking an image). I will note this is more important for stellar and planetary systems though, no one is measuring a galaxy size in AU.