Plumbing – What’s this top part of this faucet used for

Does that whole round bulb part unscrew? It kinda looks like it might. Might spray some lime away on the whole works to get a better idea how it's put together. It looks like maybe the white part should unscrew. Like the white was the aerator but the screens have been pushed out.

As the comments have pointed out, that is a compression fitting and not a threaded fitting. Removing it should be relatively easy. Loosen the nut by holding the valve with one wrench and turning the nut with another. Once it is loose enough, the valve should just pull off the pipe.

You will have to examine the exposed portion of pipe once you remove the valve to determine if you can re-use the pipe and valve as-is or if you need to cut it inside and install a new stub that you can then install a new valve on. I doubt you will be able to re-use it (its damaged already, hence the leak), so in all likelihood, you will have to replace it. If you do replace it, get a ball valve (1/4 turn) as they are more reliable and easier to operate.

Hopefuly you have an inside shutoff valve for this. If you don't, you will want to ensure you have everything you need before starting this project as the water to your house will be off. If you do have a shutoff then just close it and you can take as much time as you'd like.

Note that you should not use pipe tape or dope on compressing fittings.