CHEMISTRY COMMUNITY

I get the individual definitions of Degeneracy and Entropy, but what is the significance of their relationship with one another?

Entropy can be seen as the a measure of the randomness of a system, as the system can be in one of multiple possible states. Relating to this, degeneracy (W) is the number of ways in which a given energy state can be achieved. In other words, it is the number of possible microstates, which all have the same energy.