win32k.sys is responsible for handling USER and GDI requests.
The win32k driver is a critical component in the graphics stack exporting more than 600 functions. It extends the System Service Descriptor Table (SSDT) with another table called _W32pServiceTable. This driver is not as big as the main kernel module (ntoskrnl.exe) but its interaction with the user-mode is just as important. The service table for win32k contains less than 300 functions depending on the version of Windows. The win32k driver commonly transfers control to user-mode with a user-mode callback system. The interface between user-mode modules and kernel-mode drivers has been built in order to facilitate window creation and management.
Detailed information: http://mista.nu/research/mandt-win32k-paper.pdf