What exactly does REST mean? What is it, and why is it getting big now?

This is what REST might look like:

POST /user
fname=John&lname=Doe&age=25

The server responds:

201 Created
Location: /user/123

In the future, you can then retrieve the user information:

GET /user/123

The server responds (assuming an XML response):

200 OK
<user><fname>John</fname><lname>Doe</lname><age>25</age></user>

To update:

PUT /user/123
fname=Johnny