What do the groups represent? I don't understand them.

If you selecte several parts and group them(by pressing J key or click on the group icon in the left toolbar) you will see the group in the groups tab. You can make many groups and you can also make a group of existing groups(so you get sub-groups). Hope it helps a little?

What's the purpose of having them?

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.

And why are Baron Von Barron's arms locked while the rest are not?

Do you mean the upper body part when you add it from the library or do you open a mini figure? It depends on how the groups were configured when the creator saved the file. By default the upper body assembly is unlocked.

Or is it the upper body assembly that is locked when you load it from the library?

When I choose the upper body part of Baron Von Barron from below, the arms are locked, and I have to manually unlock them.

Ah yes I see that now, it is probably because it got the hook on the left arm! I just checked the assembly and it's using another setup(84638) then the usually assembly with two hands(76382). I think only Scrubs can change it, if it's possible? I also notice that the assembly is quite old(no. 145 in the end of the name, 76382a145 means it's the 145th added torso decoration, today we are up on no. 1499) so maybe things have been changed since it was added.

Was that a question for me?

This is effectively a very old assembly. I don't plan to modify it as this is not a bug. It will be corrected whenever this assembly will be converted to the new part system.

By the way, thank you for the video. I keep the link in mind if similar questions are asked again.