The links are “cleaner” and more descriptive, improving their “friendliness” to both users and search engines.
They prevent undesired “inline linking”, which can waste bandwidth.
They hide the inner workings of a web site’s address to visitors, which can prevent them from discovering query strings that could compromise the site.
The site can continue to use the same URLs even if the underlying technology used to serve them is changed (for example, switching to a new blogging engine).
There can, however be drawbacks as well; if a user wants to modify a URL to retrieve new data, the rewrite engine may hinder the construction of custom queries due to the lack of named variables.