What are clean urls and why do they help search engine listings?

Question
What are clean urls and why do they help search engine listings?
Answer
Clean URL's generally appear as legible text in a web site address.
For example you may have seen this:
http://www.mydomain.com?cat=2&prod=45

The link above is not clean, it would be better to see.
http://www.mydomain.com?mens-clothing/grey-trousers

The link above is an example of a clean url. It has taken the values needed to display the page and changed them into english. This can now be indexed and will help with your search engine listings.