MySQL, I think I want to use it, but I dont know where to start...

Okay, so I will try to give you as much info as I can first:

I am renting a server from Brohoster (256 slot or whatever) and I saw stuff from a bunch of plugins called MySQL database. All I knew was that it was a database... So I looked some stuff up and didnt learn enough to care about it. Now I looked it up again because I found out brohoster supports it for free. I have no clue how to set it up or how to manage it.

What does it do? What are the pros/cons of using it? Will it help me keep stuff organized or easier to manage? What tutorials are available?

I want a place where I can put the data from all my plugins and manage it in one place.