What are these things called in a bode plot
K is the gain, and w0 is the cutoff or corner frequency.

For many purposes, frequency is normalized to the cutoff, which is then at (unitless) 1.0.  Many filter design equations work the same way.  The axis stating at 0.1 is simply because you can't show zero on a log scale.  If anything interesting were going on down there, they would have went down to 0.01 or lower