If for example you want to move a Minifugure without having to select all the separate parts you can easily just with one click select the group(all parts) and move it. If you import a Minifigure to your model it will automatically become a group.
The upper body part 76382 have two groups inside it, one for each arm and hand. So if you select and want to move one arm, the hand will automatically follow the movement of the arm.
All assemblies you add to your model will add a group because they contain several parts. For example the Lower body assembly 73200, are made of three parts, hips 3815 and two legs 3816 and 3817. If you move the hip part, you want the legs to follow, right? (in most cases...)
Another purpose could be if you build a large scene, for example a street with some cars and other props, you can group each prop so you can move them individually without selecting the wrong parts.
Another use for groups is if you build a real Lego set that includes B or C models of the set, you can build all the models in the same Mecabrick model and make groups of them so you can hide and show each model individually.
I am sure that there are many more clever usages for groups that others can fill in with here if they read this thread...
Here's a quick video i made showing an examlpe of working with groups on a Minifig.