# Visualizing the hinge loss and 0-1 loss

I have seen the plot below in many textbooks before. What do the X axis and the Y axis represent exactly? What does it mean for the Hinge loss to "touch" the 0-1 loss on the (x,y) pair (0,1)?

If helpful, the source of this picture is from the entry on Hinge Loss on Wikipedia.

The x-axis is the score output from a classifier, often interpreted as the estimated/predicted log-odds. The y-axis is the loss for a single datapoint with true label $$y = 1$$.
In notation, if we denote the score output from the classifier as $$\hat s$$, the plots are the graphs of the functions:
$$f(\hat s) = \text{Zero-One-Loss}(\hat s, 1)$$ $$f(\hat s) = \text{Hinge-Loss}(\hat s, 1)$$