Sony Shared Library: It provides more functionality to VAIO applications by enabling those applications to send commands to affect the hardware of the system.
The above is the simple explanation. Basically, what the shared library does is provides an interface between VAIO applications and the device drivers so commands can be passed to the drivers to affect the hardware.
Most laptops have this ability through the combination of the Function (Fn) key and the F keys at the top of the keyboard. VAIO also provides specific power management to systems for special thermal control and additional functionality for added hardware like my keyboard backlight. I also have a light sensor that gives power management for my screen brightness and whether to turn that backlight on. As a robotics engineer, autonomous functionality like this is pretty cool!