VRAM is the memory that lives on the GPU, as opposed to the system memory attached to the CPU. When you run a model locally, the weights have to fit in it, along with the extra space the runtime needs for the context and for temporary tensors. If they do not fit, the process either fails or spills into slower memory and crawls.
The rough arithmetic starts with the parameter count. At full sixteen-bit precision, each billion parameters costs about two gigabytes, so a seven-billion-parameter model needs on the order of fourteen gigabytes before any context. Quantizing to eight bits roughly halves that; four bits quarters it. The directory lists a VRAM figure where a source provides one, and treats it as a floor rather than a guarantee, because context length and batch size push usage above it.
Two failure modes are common. The first is buying exactly to the number and discovering that the context you need does not fit. The second is trusting a total parameter count on a mixture-of-experts model, where only part of the weights are active per token but all of them still have to be resident.
If a listing has no VRAM figure, that is a signal, not a promise of "small." Check the model card, and size on hardware you can measure. See open source and proprietary models.