Rooting allows access to the file system, installation of all sorts of extra apps that can do extra things and generally more control over the device. You can put customised versions of Android on (if one has been developed for it, of course; being a Tab A I would say there are a few out there). Rooting as always a bit of a brain-overload for me (early phones) and now I can't be bothered, but if you're techo-minded, it can be great fun.
For a misbehaving system such as yours, I'd just do a factory reset to start with. You can also boot into a really basic mode using a combination of the buttons (differs with each device) so you can clear various bits/caches of the OS.