JE89, a little further explanation of the word “degree”. It actually has two meanings. The original meaning was that of a level, or stage, of membership. For example, we say that Ancient Craft Masonry has three degrees: Entered Apprentice, Fellowcraft, and Master Mason. It didn’t take long for this meaning to be extended to the ceremony by which one attained the various levels, so that more often, when we refer to the Fellowcraft degree, we are talking about the ceremony of promoting an Entered Apprentice to the degree of Fellowcraft.
Martin, being still in the process of completing the Ancient Craft degrees, does not address the other degrees of Masonry. I avoid using the term “higher degrees” as all loyal Masons are in agreement that the Master Mason degree is the highest degree; all others are additional. The York Rite consists of 7 degrees and three “orders” (which are the same thing as a degree). The Scottish Rite consists of the 4th to the 33rd degrees. The 32nd is normally the highest degree conferred; the 33rd is reserved for those who have made great contributions to Masonry or to their community, state or nation. Thus, the 33rd is actually a sort of reward or distinction granted in recognition of excellence, as you asked about in your inquiry.
There are also three degrees in the York Rite which are conferred only on those who have been elected to preside over one of the bodies. The Past Master degree is conferred, either shortly before or during the Installation of Officers, on a new Master-elect and is required before he can be installed in office. There is an equivalent degree in the Royal Arch Chapter, where the High Priest-elect must be Anointed, Consecrated, and Set Apart to the Order of High Priesthood in a Council of Anointed High Priests (this does not exist in all jurisdictions). And a similar degree, the Past Thrice Illustrious Master Degree, conferred on a new TI Master of the Council of Royal and Select Masters. (This also does not exist in all jurisdictions.)