How to read these graphs and what are they called?
This depiction is a ribbon diagram of a protein structure. It shows the protein backbone (alpha carbons and the peptide bonds) smoothed out to a continuous line. In certain areas where the protein adopts alpha-helices or beta-sheets, these are indicated by the elaborate spiral in your picture (alpha-helix) or a wide, flat arrow (beta-sheet; not present in your structure). These depictions are supposed to give you an idea of what the protein looks like.

I would assume the two arrows in the bottom to be two of the coordinate axes of the crystal since ribbon diagrams are typically obtained from crystal structures. However, I cannot know without additional information (e.g. in a footnote of a picture).