Prestige is a measure of a players activity and helpfulness. You earn prestige for tributes, reinforcing, training troops and a whole bunch of activities. 

Unlike power, any Prestige you earn only lasts for 7 days before expiring, therefore prestige can go up or down and is a rolling count of a players last 7 days. If you do no activity for 7 days your prestige will be zero.

Players on the alliance roster can be sorted by prestige and this can be used by Leaders to decide (if they wish) who to keep, promote, demote or kick to make room. It can also be seen on a player's profile page and is a good tool for those looking to recruit as it is a measure of how active someone is and how quickly they are progressing.