Labels serve as a "filter" for your PMs, and work similar to labels in GMail.
If I label several PMs with the "Administrative Stuff" label (that I make), for example, then later if I want to read all the PMs that I labeled with that tag, then I just click on the label (it will appear on the left of your screen after you make one) and all of those PMs will show up in the main body of your window.
Note that any message that is labeled is still sent to your inbox, and will still appear as a regular PM in your inbox.
The rules allow you to further customize what happens to your PMs. I typically use them in conjunction with the labels, but there are other things you can do with them, and that's something you should explore on your own, to see if it fits your needs.
Rules require you to select a criteria, and then an action associated to the message if the criteria is met. For example, if you choose a criteria of "Sender Name" and write "Vekseid", then choose an action of "Label Message with" one of your labels, then every message that Vekseid sends you will automatically be labeled with the label you chose.
If you need further help, please feel free to PM me with questions.