The "dedicated" video RAM on an integrated graphics system such as the Intel 620 you have is the amount of memory permanently taken from your system for the integrated graphics.
Under normal operation the drivers will allocate "shared" RAM in order to work. The fact that both dedicated and shared RAM is you system RAM means that there will be no difference at all between them beyond what they are named and whether they were allocated by the computer firmware or graphics drivers.
The dedicated RAM is likely only useful on a system without proper drivers.
It is where the graphics chip will work on the main screen buffer away from the rest of the system. You will need a minimum amount of memory for the chip to work but the only time increasing it is going to be useful is when you have one or more high resolution screens connected.
With proper drivers the benefit of increasing it will quickly vanish, especially if you don't have a lot of RAM available to begin with and loosing another 256MB could mean that has less memory to do other things.