Jakob Nielsen answers these questions (and the How and When actually) in his Alertbox Column. If you don't have the 5 minutes to spend reading it, you can read the definitions below and then get back to reading it when you have time :)

What is usability?

It is a quality attribute that accesses how easy user interfaces are to use.

Why does it matter?

To put it simply, if a website is not easy to use, people don't use it. People are usually in a hurry on the web, so every time you make them think how to use your website, they get frustrated and leave (maybe to not come back again).

Where can I learn more?

I'm still quite a novice on the usability subject. These are two resources that I used, trust and recommend:

Alertbox Column, by Jakob Nielsen. This is the best free online resource by one of the most known authorities in usability. There are hundreds of articles here, just read them one by one.

Don't Make Me Think, by Steve Krug. This book is a very enjoyable reading and I'd recommend it for everyone, expert or complete beginner alike.  
  
You can also take the recommended reading advice from Steve Krug itself.