You can surf the web but it is only limited to text-based websites, like Google, Wikipedia, Gmail, etc.
And yes, you still have to buy books onto your Kindle device. Ebooks on the Kindle are cheaper than actual books though.
Guess you are considering to get the Kindle, am I right? I own the Kindle 2, so let me give you some of my opinions about it. I've to say I love it! I think I've read over 30 books with my Kindle, no glitches so far! I think I've saved over $100 on buying these 30 books, as they are cheaper than actual books.
One of the reasons I love my Kindle is that it has helped me improve a lot on my efficiency and utilize my time. Before I have the Kindle, waiting time like when I'm waiting for friends or waiting for shuttle bus or some thing like that is simply wasted. Now I just need to bring the Kindle 2 along with me, and all my favorite books are inside it. Another thing I like the most is the text-to-speech function, which means I can "read" books without even holding or looking at the Kindle. Now I like to use this function when I've myself busy on some boring things, say when I'm on the step machine or doing some housework...
I like reading and at the beginning I did miss a bit on the feeling of reading books. But now I love to hold the Kindle, the e-ink seems to work very well, it is really like reading books... Now I often read with the Kindle for several hours but I don't feel tired... And I now prefer to manage all books inside the Kindle rather than my never big enough bookshelf... And like to do bookmarking, annotation, dictionary lookup without any additional thing but a Kindle.
There are quite a lot of free books (tips: if you're outside the U.S. all the books will have US$2 added, but when you choose to download to computer when you check out, the $2 will be waived, and you can copy the books to your Kindle through USB cable), and many Kindle books, magazines and newspapers are cheaper than the actual paper version. I remember I read these reviews about the benefits of the Kindle when I decided to buy it:
http://www.amazon.com/gp/redirect.html?ie=UTF8&location=http%3A%2F%2Fwww.amazon.com%2Freview%2FR2DUM7S4XW06QN%3Fie%3DUTF8%26ASIN%3DB00154JDAI%26nodeID%3D%26ref%255F%3Dcm%255Fcr%255Fpr%255Fcmt&tag=moreinfo-po-20&linkCode=ur2&camp=1789&creative=390957
http://www.speedreaderxreview.com/is-kindle-2-worth-the-price
Finally, in case you don't know, Amazon has just put a price slash on the Kindle 2, and it is now selling $100 cheaper than the price I got my Kindle, and it adds in international wireless access and native PDF support... So take the chance if you want it.
Hope it helps :)