It's just the name of the Space Station. "Deep Space" for being far-ish away from Earth, "Nine" because writers wanted us to think that there were multiple similar stations.
There's no special scientific meaning behind it, although "deep space" does crop up in real-world science. The problem is, no-one there seems to agree on what it means either.
Terok Nor was a space station of Cardassian design that was built in orbit of the world of Bajor by Bajoran slave labor in the year 2346. The station was used for the processing of uridium ore by Bajoran laborers.
Status: renamed Deep Space 9 (2369-2373, 2374-2383)
Facility type: space station
Affiliation: Cardassian Union
Class: Nor-class