OMS2 is the burn of the Space Shuttles' Orbital Maneuvering System that circularizes the orbit after launch. After it the shuttle was in the same orbital plane as the ISS, but some distance behind. To catch up with the ISS, the orbit was slightly lower (~ 80 km) and therefore faster.
The OMS2 Phase Angle tells how far behind the shuttle was. In other words, how large the distance between ISS and Shuttle was when the Shuttle entered orbit. The distance is given as an angle, which is much more convenient to deal with in a circular orbit than an actual distance. Note that it can be larger than 360°, meaning that the Shuttle is more than one full orbit behind ISS. This leads to different flight times until docking as is marked by the lighter "FD3" and darker "FD4" colour. "FD" stands for Flight Day. If the distance is small, the docking can be done on the third day of flight, for large angles a rendezvous is only possible on day 4.
There is no relation between the phase angle and the 10 minute length of the launch window. "Catching up" with the ISS is not severely constrained, there are other parameters (crew sleep and day light) that have larger influences on the flight time. The window is just 10 minutes short, because of Earth rotation: The shuttle won't end up in the same orbital plane as the ISS if launch is delayed too much. Some discrepancy can be compensated for by altering the launch trajectory and steering slightly off-course. But there are limits due to additional fuel needed and the load on the external tank if the shuttle has to fly at an angle and not straight ahead.
The two constraints of phase angle and planar window are independent from each other and sometimes don't overlap. For example, there is no FD4 opportunity on Apr 26 and some launch windows are cut short because the phase angle would be too large (i.e. > 584°).
There's a very detailed description in this document, an example ISS rendezvous is described starting on page 225: