One of the things that creates a sense of space is the way our ears hear sound, given that we have two of them.
If you think about how our ears locate sound, there's a delay between one ear and the other - that is, the sound doesn't arrive at exactly the same time, especially depending on where something is placed.
I've been recording with a stereo microphone setup (two SM57s), though I honestly could be doing a better job with varying my location when singing into the microphones.
I know another more basic thing is just to vary the pan of each track. What I've done in the past is actually record two tracks, put a delay on one, and then adjust the volume until it sounds like it's realistically coming from a direction. There are some spatial audio plugins as well.
What I'm trying to personally get better at is thinking about this in the context of having stereo speakers, rather than headphones.