An affine transformation is a function that maps one vector to another.
In the following example, we'll create an affine transformation that translates an x and y coordinate such that every point is moved right 10.
def moveRight(x, y): return (x + 10, y)
If we apply this function to every point in a grid, we have effectively moved that entire grid to the right.
Why this is cool
This gives us a pretty neat abstraction for moving, rotating, or reflecting 2d or 3d objects.