What is root and why do i need it ?
"Root" is the common way to refer to the fact to the user account which has superuser rights on the device. Superuser rights imply full control over your phone's capacities, which are determined by the software and the hardware of the device. Non-superuser accounts have limitations, usually established for the sake of software security (for example, not allowing a user to disable critical functions such as phone or GPS), hardware safety (not allowing to change the processor's frequency speed, aka overclocking the CPU) or, in some cases, for someone's profit (disabling wi-fi tethering is a typical one as users are forced to buy data plans in order to use their devices to tether). In Android's case, Superuser is composed of an app* and a set of instructions to give this app root rights.
How do i get Root ?
Ways to get Root on xperia play or other xperia 2011 range device's
1) SuperOneClick (Recommended) ( locked or unlocked bootloaders )
SuperOneClick the easy way to root your xperia 2011 with locked or unlocked bootloader's. curruntly working on any 2.3.? software and now has the zergRush method built-in.
Downloads and info available @ http://shortfuse.org/
2) Easy rooting toolkit created by DooMLoRD ( locked or unlocked bootloaders )
doomlords easy rooting toolkit for all sony ericsson 2.3.? software this software will.
(1) root ur device using latest zergRush exploit
(2) install Busybox
(3) install SU files (binary and apk)
Downloads and info available @ http://forum.xda-developers.com/showthread.php?t=1319653
3) Gingerbrake app created by chainfire ( locked or unlocked bootloaders )
This is an installable app that will automaticly root your device (only will work on sony ericsson xperia gingerbread version 2.3.2)
Downloads and info available @ http://forum.xda-developers.com/showpost.php?p=13086954&postcount=1
4) Rootxperia.zip created by free xperia team (for unlocked bootloaders)
This update zip is to be installed by clockwork mod recovery and will automaticly root and install super user app and busybox. This method will work on any gingerbread xperia software.
Downloads and info available @ http://forum.xda-developers.com/showthread.php?t=1130639
For other ways if you have tried these already see this thread ( More ways of rooting xperia ) thanks to CrimsonSentinel13.