In a dense model, every parameter takes part in processing every token, so the active count equals the total. In a mixture-of-experts model, a router sends each token to only a few experts, so only a fraction of the total parameters is active at any step. A model with 100 billion parameters in total might use 10 billion for each token.
The number matters because computation per token, and therefore much of the speed and energy cost of generating text, follows the active parameters. That is why a large mixture-of-experts model can run about as fast as a much smaller dense one.
It does not reduce memory needs. All parameters must still be stored in fast memory, since different tokens use different experts, so hardware requirements follow the total count.
When models are described, look for both numbers, use the active count to estimate speed and cost, and use the total to plan memory.