What is CVG in turbofan engines?
CVG stands for Compressor Variable Geometry. (e.g., this pdf, page 5).

This is a technique to change the pitch angle of the compressor vanes, much like a variable pitch propeller. Wikipedia does not have an article for the use in aircraft (probably because it's not used all that much), but does have an article on a Variable-geometry turbocharger which is closely related (for non-car-enthusiasts: a turbocharger compresses inlet air with help of a turbine at the exhaust). Basically, this system lets you control the pressure ratio independent of the RPM. Advantages include


More efficient settings based on air pressure (altitude / temperature). You basically decouple the turbine stage from the compressor stage (but instead of a gearbox, you use the vane angle). This way, you can optimize your compressor stage to different conditions while keeping the turbine RPM at the most efficient value.
More efficient cruise performance without compromising TO/GA capabilities. Aircraft engines are heavily overdimensioned to account for take-off power and contingencies, which means a bigger engine than strictly necessary and thus less efficiency in cruise. This can now be partially mitigated by varying the compressor vanes pitch for optimal efficiency during cruise and optimal power during TO/GA
Higher engine RPM possible during approach. Normally, to keep your engines spooled up for eventualities, you need to increase their power, and as such need to increase drag with flaps and spoilers to keep the speed down. Now, you can spool up the engine to a high RPM with low compression ratio, and increase power relatively fast without having to overcome engine inertia by increasing the compression ratio by increasing the vane angle.