PSR stands for PHP Standards Recommendation. These standards are created and maintained by a group of PHP projects who have a common goal to create a uniform standard for writing PHP code. They call them self Framework Interoperability group (FIG). This group have different kinds of voting members which are not only framework developers like Symfony, Lithium and CakePHP. Each of them have a representative as a voting member. But also phpDocumenter and even composer have their representatives.
Currently there are 9 accepted standards. Each has its own purpose. The most important ones which cover coding standards and coding style are PSR-1 and PSR-2. Then we have PSR-4 which replaced PSR-0 that covers a standard for an auto loading class.
And then we also have PSR-3, PSR-6, PSR-7, PSR-11, PSR-13 and PSR-16.
You wonder, why some numbers missing? Well those are ones that are still in draft.
I recommend reading and following these standards. If everyone follows this, then all shared PHP code will behave and look the same on a high level. This is a good thing for every developer. If every third party library use different naming conventions and character encodings then it would all be a big mess.