Frameworks in PHP now exist in all shape and forms, because all PHP developer have always been developing their own "framework" until a few of them got really popular.
Frameworks in PHP are good for a few things:
* readability and structure of your code (MVP, templates, ...)
* normalization of libraries (Facebook SDK, analytics, queues, ...)
* libraries for low-level layers of the code (DBs, sessions, ...)
After 12+ years playing with this language, I started re-using one I named Snow when working for the agency RIVER, and the aim was to be able for anyone to understand all of it within minutes and have it non-constraining to support any app or site: https://github.com/fellowshipofone/Snow
Now, for the past year or so, I find that the most elegant with highest performance framework is Yii. It also is more complex, but seriously worth looking into if you have a fairly big custom project. http://www.yiiframework.com/