In https://deepai.org/machine-learning-glossary-and-terms/affine-layer I have found the following:

"Mathematically, the output of an affine layer can be described by the equation:

output = W * input + b

where:

• W is the weight matrix.

• input is the input vector or matrix.

• b is the bias vector.

This equation is the reason why the layer is called "affine" – it consists of a linear transformation (the matrix multiplication) and a translation (the bias addition)."