It depends on what program you’re using–Smoothing groups are actually just a 3ds Max thing, a number assigned to a set of polygons that determines which polygons are smoothed together. Like on a cylinder, the sides would be smoothing group 1 and the top and bottom would be smoothing group 2.
Other programs use their own form of smoothing that aren’t called smoothing groups, and all programs have some kind of system for that.
Smoothing settings are important because at the very least it’s a way to make curved surfaces look smooth and rounded where otherwise you would see the polygons like facets on a jewel. What’s important is that it changes the normals of the object, normals are the direction that a surface is facing, so for things like normal maps it needs to make sure that the smoothing/normals are correct or the normal map won’t look correct.
And you need correct smoothing no matter what you’re doing.