"A break" can mean a few things, but in this context, it normally means either a scheduled break in continuity or an interruption to normal continuity. When the break is defined or intentional then it is normal to say that you are "on" that break.
You give the example of a "commercial break" on TV which occur during programming to allow for commercials to be shown. These have a defined beginning and an end. They are often announced by saying "Let's take a break". During that time you could say that the program is "on a commercial break".
It is similar to the way people speak of vacations (which is also a "break" from work, or your normal routine) - you take a vacation, and during it you are spoken of as being "on vacation".
Note that there are other, more idiomatic ways of stating that a programme is currently taking a commercial break, such as "it's gone to commercial".