Think of it this way. There are four basic qualities: hot, cold, wet, dry, which in combination produce 4 elements: Earth Air Fire, Water. There are three modes in which those elements express themselves: Cardinal, Fixed, Mutable. Each Zodiac sign can be understood as one of the 12 possiblities (3x4) So Libra is another name for Cardinal Air.... and using the symbols of Libra allows us to refer to all of the things implied by Air and Cardinality. The Decans take it a step further. Each of the 12 signs is further divided into 3 decans: Ascendant, Succedent, and Cadent which sort of map the territory of the sign. Which is why the first 10 degrees, the 2nd 10 degrees, and the 3rd 10 degrees of Libra are all distinct.
So... working backwards you have 36 decans with are 12 groupings of 3 (Ascendant, Succedent, and Cadent)... And those 12 are in turn grouped by Mode and/or Element. It's a way of breaking down the manner in which stuff manifests.