Symfony is a rather popular PHP framework; it is commonly regarded in the PHP community as one of the higher-quality frameworks (amidst many half-baked frameworks that cause serious problems once your use case moves past the blog tutorial).
In terms of functionality, it's basically for PHP what Rails is for Ruby, but unlike many other PHP frameworks, it's been designed with the platform in mind rather than trying to force Rails' concepts into PHP, as a result if which it feels "just better". This has given it an edge over competitors, which is why Symfony is remarkably popular among the more professional PHP businesses.
I think it's basically the only mature and popular surviving framework that dates from the blast of PHP frameworks that came to be when Rails got popular and PHP coders wanted that too.
Symfony is closer to django than to rails (in terms of APIs, I believe the project itself is built in a more modular manner) though, many of symfony's features are almost straight ports of django features, sometimes renamed.
I have not seen a greenfield, or even brownfield, CakePHP or Zend project in years, outside of $BigCo environments. Calling CakePHP in particular a "market leader" seems rather wrong.
Zend is well-written and solid, but old; it hasn't been materially upgraded for PHP5.3--which is all you should be using these days, there's no good reason not to.
Symfony2 can trivially use Zend-based components. (It does, for some tasks.) I've heard it wise-assedly called "ZF3" because of its compatibility in the past.
In terms of functionality, it's basically for PHP what Rails is for Ruby, but unlike many other PHP frameworks, it's been designed with the platform in mind rather than trying to force Rails' concepts into PHP, as a result if which it feels "just better". This has given it an edge over competitors, which is why Symfony is remarkably popular among the more professional PHP businesses.
I think it's basically the only mature and popular surviving framework that dates from the blast of PHP frameworks that came to be when Rails got popular and PHP coders wanted that too.