I get the output of the model (y_model = m*xs[i]+b), it's the y = mx + b where we know x (from the dataset) and have y be a variable.
The error is where I start to lose it, so I get the idea of the first part (ys[i]-y_model). It's basically the difference between the actual y value (from the dataset). I get that we want this number to be as small as possible as the closer to zero it is for the entire dataset that means we get closer to the line going through (or near) all the points and the closest fit will be when this total_error is nearest to zero.
What I don't get is the squaring of the difference. Is it just to make the difference a larger number so that it's a little more normalized? How do you get to the conclusion that it needs to be normalized? Same thing with the learning rate? I believe these to be correlated but I can't tell you how...