What is squared about them? You have a number of units times a different number of units in the numerator. Does that make the units, units squared?
The units of Cov(X, Y) are the units of X times the units of Y.
If X is measured in cubic centimeters and Y is measured in degrees Fahrenheit, then a typical term in Cov(X, Y) will be (Xi – μX)(Yi – μY); the units of Xi – μX are cc and the units of Yi – μY are °F, so the units of the whole term are cc_×_°F. The units will be _something_² only when X’s units and Y’s units are the same (both something).