A graphics card is a dedicated piece of hardware that deals with the output of the computer that is visually displayed to the user. It controls the operating systems desktop, programs that run, as well as 3D manipulation of objects, as used by for example games. Graphics cards range from small, low-powered devices to huge, power-hungry ones as used for high-end gaming or demanding professional workloads.
A graphics card is a dedicated piece of hardware. This typically takes the form of a dedicated, discrete GPU card that plugs into the motherboard and has its own video outputs - which the systems monitors should be plugged into. dGPUs are the main form that GPUs occur in PC, and for gamers or professionals who want GPU performance there is no other option.
High-end gaming GPUs can draw lots of power, and often require their own power cables to work at all, however many low-end ones will work with just the power they are able to draw from their interface slot - usually PCIe, which allows up to 75W max from the PCIe slot. This high power draw also creates lots of heat, and powerful GPUs will often have very large heatsinks as well as fans to dissipate it.
A graphics card is a dedicated piece of hardware. This does not mean it is a standalone piece of hardware though. Many modern CPUs also come with a dedicated GPU built into them, referred to as an Integrated GPU, or iGPU. (because it is integrated into the CPU, instead of a standalone component). iGPUs are mostly used because a CPU with an iGPU is often less expensive than the combined price of a conventional CPU (with no iGPU) and a discrete GPU. Furthemore, iGPUs are not recommended for gaming though, with really only the most powerful iGPUs being able to handle modern games, and even then, gaming at high settings or at resolutions above 1080p are really beyond iGPUs, and gamers should look at actual dedicated gaming GPUs for gaming, rather than iGPUs.
PGPUs have VRAM (Video RAM) built into them. This VRAM allows the GPU to store information on board itself, and not have to use system memory (RAM) to store information. VRAM is used for normal operation of a GPU, however some computers GPUs, especially on laptops, low-end, or older devices may use the systems RAM instead of having their own dedicated memory.
The main use of lots of VRAM for modern GPUs is to store the textures used for games. How much VRAM will vary depending on the game, as each game will use its own textures. In addition many GPU reporting programs will list the amount of VRAM the game has requested to use, and the GPU has reserved for that game, instead of how much of that it is actually using.
A GPU with more VRAM will generally not perform better than one with less unless the textures for the game in question are sufficient to fill the VRAM of the GPU with less VRAM, in which case the juggling of textures can cause an extreme performance hit whilst the GPU has insufficient VRAM. More VRAM will make the GPU more expensive, and cause it draw slightly more power, and thus create more heat, however more VRAM is generally always better to have, if possible, although cards with more VRAM are not always the best option financially, as the extra VRAM may not be useful for the useful performance range of the card.