Individual Prestige is the average of the PI (power index) of the top 5 champions of each player. Improving the Hero Rating of those 5 Champions will increase your Individual Prestige.
Your Alliance Prestige will be the average Prestige across the Alliance. It is initially calculated based on the average of the Individual Prestige of every Member in your Alliance. This means that Members leaving or joining the Alliance will modify the Alliance Prestige value.
This value is very important for Alliance Quests as it will determine the difficulty of the opponents. The higher the difficulty, the more Points you will earn per battle! This will allow your Alliance to place higher in the Event and hit Milestones faster.