A graphics card or GPU is an expansion card which can be inserted into the PCI slot and is used for high end graphics intensive requirements on your computer.
Motherboards come with intel or AMD integrated graphics from the CPU and motherboard. However if you want to play games you may need a graphics card. The advantages of a Graphics card is that you will be able to get better performance than using integrated graphics and things will be smoother as a result.
If you have a laptop or a prebuilt all in one pc your options for expanding and adding a gpu may be limited. This may be dependent on size and voltage of your Power Supply Unit. There are two major manufacturers Nvidia and AMD and offer similar offerings.
The GPU is dedicated to rendering exclusively and is the most powerful part of the computer. Video memory is how much dedicated RAM the GPU has for rendering. Video memory is used for storing high resolution textures and post processing effects. The GPU has two buffers one is dedicated for pushing frames to the monitor and the second is for maintaining the framerate. This process is reversed to keep the memory running constantly.
An older 2gb card will be equivalent to a newer 512mb card so newer cards are usually the best choice. Playing games at high settings may also require more video memory for example low graphics setting will require less power. High and ultra settings will require more video memory.
If the GPU in Question runs out or Video memory it will start using the computers ram just like integrated graphics.
Higher resolutions like playing games in 4k will require multiple and higher video memory cards. SLI and crossfire offered by Nvidia and AMD allow multiple cards to be run at once. However both cards need to be the same type. For example two GTX 1070 can be run in sli .
However a GTX 1070 and a 980 cant be run in sli because they are different cards also you can mix AMD and Nvidia cards.