When "pride goes before a fall" it means that arrogance usually proceeds some kind of failure. Pride is taking joy in one's admiration. Humilty is the opposite of pride, it's about being modest and not indulging in admiration of the self. The word fall means to move downward, or to lose balance and collapse. Fall can also be used to describe the season between summer and winter. The joke is centered on the word fall and its different meanings.
If pride goes before a fall , humility should arrive by that winter