A dispersion diagram is a plot of frequency (usually in radians per second) on the vertical axis, against wavenumber (usually in radians per metre) on the horizontal axis. In vacuum it is a straight line through the origin and the slope is the speed of light. In other materials it is different to this. The speed may not be the speed of light and may vary with frequency. The local gradient is equal to the phase velocity, which is the speed the pattern of electric or magnetic field can be measured to travel (like Moire fringes), and the ratio frequency/wavenumber is the group velocity, which is the speed that information or power travels.
If the material is periodic, the pattern repeats itself, along the horizontal axis, and the diagram only shows one period. It can be different in different directions, and sometimes one period in the x direction is plotted, followed by one period in the y direction then one period across the diagonal.