Some points that I consider important and relevant to the use of friendly url
Raking on search sites
Search engines handle dynamic url (my-page.php? post=1234) other than static url (my-page/post/url-friendly), so it can help improve the page ranking.
Content description
When reading a friendly url (stackoverflow/quao-important-and-use-url-friendly) the user already knows what will find on the landing page before even clicking, unlike reading (stackoverflow/21943), but note that in this case, to facilitate the implementation can be used (stackoverflow/21943/quao-importante-e-usar-url-amigavel)
Memorization
Users can more easily memorize a url (my page/brand/product) than (my page/1234/3887929), in this case a phrase can become a url (sports/world cup-2014/round goals), this facilitates the user to directly reach the desired page and still understand the content of the landing page.
Publicizing
A friendly url makes it easier to be disclosed, whether by phone, banner, printer, card and etc...
porém existe um custo de tempo pra desenvolver e dar manutenção em algo assim.
If you’re developing this, you’re reinventing the wheel.– Oralista de Sistemas
Another thing: take a look at the URL of this question itself. I believe that there you will find the best answer ;)
– Oralista de Sistemas