So... it's not R1 itself.
It's a model called Qwen, trained by Alibaba, which the DeepSeek team has used to "distill" knowledge from their own (100x bigger) model.
Think of it as forcing a junior Qwen to listen in while the smarter, PhD-level model was asked thousands of tough problems. It will acquire some of that knowledge and learn a lot of the reasoning process.
It cannot become exactly as smart, for the same reason a dog can learn lots of tricks from a human but not become human-level itself: it doesn't have enough neurons/capacity. Here, Qwen is a 7B model so it can't cram within 7 billion parameters as much data as you can cram into 671 billion. It can literally only learn 1% as much, BUT the distillation process is cleverly built and allows to focus on the "right" 1%.
Then this now-smarter Qwen is quantized. This means that we take its parameters (16-bit floats, super precise numbers) and truncate them to make them use less memory space. This also makes it less precise.
Think of it as taking a super high resolution movie picture and compressing it into a small GIF. You lose some information, but the gist of it is preserved.
As a result of both of these transformations, you get something that can run on your local machine — but is a bit dumber than the original — because it's about 400 times smaller than the real deal.