As others have said, the primary purpose of the clip is to route cables along the shafts of light stands.
The two holes are for using Allen-type wrenches to help leverage spreading the clip when installing it onto or removing it from the shaft of the light stand. They're not really needed if the shaft is in the lower range of diameters for which the clip is intended, but can be almost essential to getting the same clip on a shaft that is the maximum diameter for which it is made.
A typical clip is the Manfrotto 065 that is made for shafts ranging in size from 22-30mm in diameter. They're pretty easy to press onto 22mm shafts without any tools. Doing the same with a 30mm shaft is considerably more demanding. Getting the clip off of a 30mm shaft will almost certainly require some assistance. I've seen others use flat screwdrivers to remove them, but that can scratch or even bend the surface of the hollow metal shaft.
Placing the short shaft of a set of Allen keys in each of the holes with the long shafts extending more or less in the same direction opposite the opening of the clip allows one to spread the clip by squeezing the other ends of the shafts of the two Allen keys together.
The reason the small allen key receiver holes are two different sizes is so that the typical two-sized set of Allen keys needed to adjust most Manfrotto (and copycat) tripods/monopod/light stands/etc. can be used without needing a duplicate of either sized hex wrench.