What kind of ceiling is this, and what's the process like for making it smooth?
It's called a drywall stomp. You use normal drywall mud along with something called a stomp brush and it makes that pattern on the ceiling.
To remove it, take a spray bottle and fill with water. Spray your ceiling to make it damp, then take a drywall trowel and scrape the ceiling down.
It's a texture made with a stippling brush:
I would suggest keeping it because otherwise you're just creating unnecessary work for yourself. Probably can't scrape it smooth so you would probably have to replace the drywall. If you're not that good at drywall your new ceiling will look way worse than it looks right now.