What it means
Parameters, often called weights, are the numbers a model adjusts as it learns. Before training they are effectively random; after training they encode everything the model knows. Saving a model means saving its parameters.
Parameter count is the headline number vendors quote, and it is a rough proxy for capacity — larger models can encode more. But it is a poor proxy for capability. Training data quality, training duration, architecture and post-training all move performance substantially at a fixed size, and smaller recent models routinely beat larger older ones.
Parameter count does directly determine something concrete: memory. Running a model requires holding its parameters, which is what makes quantization the deciding factor in whether a given model fits your hardware.
Why it matters
Treating parameter count as a quality score leads people to dismiss efficient models that would serve them better and cheaper. The industry's own trend runs the other way — toward getting more out of fewer parameters, because inference cost scales with size.
In practice
Use parameter count to answer "will this run on my hardware," not "is this good." For quality, look at benchmarks and, better, at how it does on your own tasks.