Number of parameters is the amount of numbers that can be changed in the model. Mathematically this means number of dimensions of your optimization problem. For you as a programmer, each of this parameters is a floating point number, which typically takes 4 bytes of memory, allowing you to predict the size of this model once saved.
This formula for this number is different for each neural network layer type, but for Dense layer it is simple: each neuron has one bias parameter and one weight per input:
N = n_neurons * ( n_inputs + 1)
.