The demonstration shows that light travels at the same speed in both the glass rod and the oil. In other words, both materials have the same index of refraction.
Work Step by Step
Being clear doesn't mean being invisible: normally, you can easily spot a submerged glass rod because light undergoes a change in speed as it passes from the liquid to the glass and back again, and bends at the interfaces, highlighting the edges. In this case, no such speed changes take place, and the rod is invisible.