Basically a video card with more memory is able to store more texture maps on the card at once, thus allowing it to access the information faster without a drop in performance.
A card with less memory would need to swap data from the system RAM to get access to new textures quickly, e.g. when you open a door into a new room, a card with less memory may jump for a split second when all the textures are suddenly being transferred to the video card from the system RAM.
But don't worry, 128mb of memory on a graphics card is enough to perform well in HL2.