Was house built sometime around the 1950s? Yes it's probably rock lath and plaster. You can repair with gypsum board and setting type drywall mud. Use some self-adhering mesh tape at edges. In my house the plaster thickness is all over the place, so you sometimes need to adjust using wood shims so you don't have to put a lot of mud on. You might even have to chisel off some plaster if a joint is going to get too high.

House was built 1944

Yes, that appears to be it. Can't tell from pics, but is that vermiculite insulation at the bottom of stud cavity? If so, don't be strewing that stuff around.

I use fiberglass tape, Durabond 90 and then a lightweight joint compound to make final sanding/finish easier.

Seabornman. I do believe it is vermiculite. I've covered the hole so it doesn't get blown around.