The refresh rate is measured in Hertz, and it is the number of times a second that a frame is displayed on your monitor. 80 Hertz, means 80 frames are drawn on your monitor every second.
VSync forces Half-life to generate a number of frames that is the same or a factor of your refresh rate, depending on your performance.
Example: You set your monitor to 80 Hertz.
So, if you set VSync your frames per second in Half-life will be..80..or 40...or 20....depending on what your computer can handle.
VSync off, means that Half-life just lets your computer generate as many Frames per second as it can, but this can result in frame tear, because they are not synchronised.
Anyways, that's a basic explaination. People feel free to dispute it if you want.