The PHP Standard Recommendation is about how you should write your code so that it’ll be easily readable and usable by others. It covers topics like coding style, file organization, autoloading and standardizes various interfaces. The PSR was thought up by the Framework Interoperability Group (FIG), which came into being at the php|tek 2009 conference. Its members include the authors of various well-known PHP frameworks. The PSR is in no way “official”; it’s just that the Framework Interoperability Group (FIG) contains a nice cross-section of experienced PHP developers, who vote on whatever the best coding style should be. As such, you can follow all or part of PSR, or none of it. It’s up to you really, but some projects that you want to contribute to may require that you follow some of the PSR, just so that everyone is on the same page. There’s nothing wrong with having a standard where there wasn’t one before.
So who’s a member? There are over 20 members now (from 5 when they started), and they include the authors of CakePHP, Composer, Zend, Lithium, SugarCRM and Symphony. People who’ve been around the PHP block, so to speak.
As for the PSR standards themselves, there are about 17 of them, but only 7 have been accepted by all members. The rest are still being voted on, or have draft status [as of September 2016].
(I wrote this article which looks at PSR-1 in detail as an example.)