Technically, that is called popcorn texture. It is basically deywall mud with additives to make the bumps.

Removing is is possible, but messy. Best way is to remove/cover all furniture/flooring, use a spray bottle with plain water in it, get up to the area you want to work, spray the area(2' by 2'), wait about a minute, and scrape off the popcorn texture with a wide putty knife. You can use a small bucket/trashcan to catch the stuff.

You will then find the reason the popcorn was used---it hides all the roughness caused by not finishing the mud/tape job(saves a LOT of labor for builders) to the same smoothness of the walls.

So, opnce you get all the stuff off, you will need to do some mudding/smoothing to get a good enough surface to paint. That process i8s VERY dusty and requires a bit of experience to do quickly. DIYers can learn how to do it, but it takes days as a rule. A pro team can come in and do it in hours.

The first things to determine are: is it asbestos and has it been painted? If the answer is yes to either question you have a considerably more difficult job on you hands. Sometimes it is best to cover it with 3/8" drywall if the perimeter trim will accommodate it.

Here is a link that might be useful: popcorn

It is not that hard to remove the drywall and just replace it.

Finishing the new drywall will be the same amount of work if you tear out the old or just cover it up with another layer.

Covering also takes longer than hanging new on the joists since you can see everything (shorter screws and fewer misses).

Technically popcorn is an Acoustic Textured Ceiling. It is basically vermiculite, drywall compound and water based white paint.