What is affine transformation in regards to Neural Networks? I have been reading a paper recently on Highway Neural Networks and found the following:

$y=H(x,W_H)$
$H$ is usually an affine transform followed by a non-linear activation function, but in general it may take other forms.

After googling about affine transform I can't say I understand fully what it means. Can somebody please elaborate?
It's a linear transformation, for example lines that were parallel before the transformation are still parallel. Scaling, rotation, reflection etcetera. With regards to neural networks it's usually just the input matrix multiplied by the weight matrix.