PHP frameworks follow the MVC architecture, which means that the presentation is separated from the database and business layers, resulting is neat, clean and understandable code modules.
You are forced to stick to certain coding rules, ensuring good coding standards, which means that the code is written as it is supposed to be written and you do not run into unreadable code later on.
Most frameworks have built in checks to ensure that urls are clean. This is particularly important when you consider SEO.
Access to service APIs makes expanding connecting to other applications like Facebook and Google Maps very easy
Access to plugins means that many commonly used components need not be developed.
Automatic includes mean that you never have to worry about forgetting to manually include common files ever again.
Validation of forms and error flagging are made easy with built-in objects.
Strictly followed coding standards and code modules makes it easier to reuse code.

You may be tempted to create just one or two controllers, which, if done, defeats one of the purposes of using MVC. So, keep your controllers small and as close to the view as possible.

Although the learning curve can be steep when it comes to understanding frameworks, the effort pays off in the end – applications are a lot easier, and quicker, to develop using frameworks.

Sources: http://joshsharp.com.au/blog/view/why_you_should_be_using_a_framework, http://toys.lerdorf.com/archives/38-The-no-framework-PHP-MVC-framework.html, http://www.workoninternet.com/article_26808.html