I've had a look around and found this interview from Jon Watts, the director for Spider-Man: Far From Home, where he was asked this question, and whilst he wasn't specific he says it is a Skrull spaceship, they are in space and Fury is on a mission. He doesn't elaborate on this any further.
But where exactly is Fury?
Watts: It’s definitely a Skrull spaceship. But I don’t know if I can specifically say where they are. They’re in space. He’s on a mission, but he got to take a very brief vacation on this little relaxation pod.
Los Angeles Times, Spider-Man team spills secrets of ‘Far From Home’ post-credits scenes and Marvel’s future
There is speculation though that this could be S.W.O.R.D. (Sentient World Observation and Response Department), a subdivision of S.H.I.E.L.D. which monitors Earth for threats from above. Considering Fury's below comment in Captain Marvel, it seems likely that he would have created S.W.O.R.D. after the events of the film but we just haven't seen it yet. Though, when it was created is up for speculation, considering it doesn't seem to have had any active involvement in some of the events we've seen that you'd think it would do, therefore it could have been created after Avengers: Endgame with the help of Carol and the Skrull.
Fury: Been riding a desk for the past few years, trying to figure out where our future enemies are coming from. Never occurred to me that they'd be coming from above.
This was even teased at in Agents of S.H.I.E.L.D., though it seems to have been more of a throw away reference rather than anything more. Or, this could have even given those in S.H.I.E.L.D. the idea to go ahead and create it... we don't know.
Jemma Simmons: Fury never said anything about deep space outposts being developed, did he?
Phil Coulson: There was nothing like this in his black box.
Elena 'Yo-Yo' Rodriguez: So, wait, S.H.I.E.L.D. doesn't have a space division called S.P.E.A.R. or something?
[Couslon nods no]
Elena 'Yo-Yo' Rodriguez: Really? I always thought you guys had people hiding on the moon.
Agents of S.H.I.E.L.D., Season 5 Episode 1, "Orientation: Part One"