The learned numeric weights inside a neural network; 'model size' counts them.
Broad technical consensus on what this term means. Disagreements that invoke it are about the world, not the word.
Parameters are the numbers training actually adjusts, the weights on the connections inside a neural network. A "175-billion-parameter model" is a network with that many learned values. Everything the model has learned is encoded, opaquely, in them.
Parameter count is the standard shorthand for model size and capacity: more parameters can store more, but cost proportionally more compute to train and to run. It is a useful but rough proxy, architecture, data quality, and training technique move capability at the same parameter count.