I was told by my eye specialist that I have a cylindrical power, which is talking about what?

Astigmatism. Your specialist was referring to astigmatism which is a situation where your eye is not perfectly round like a basketball, but it is slightly ob-longed in one direction as in comparison to a football. This is very normal and almost every one has some amount of astigmatism, depending on how precisely you measure the difference in two different axis's.