Essence, also called Player Essence and sometimes known as Mana, is a resource which is given automatically to players daily. It is managed by the EssenceGlue plugin (source). The daily award is the only way to obtain essence (aside from trading with others), making it a measure of player activity and player count within a nation. It is often used in factory recipes and as an upkeep for exile pearls.
After a certain amount of playtime every day (varies by server, but roughly 30 minutes), you will be automatically awarded a certain amount of essence. This playtime does not have to be consecutive (ie, you can log out and log back in).
Once awarded, you must wait 18 hours before being able to claim again. After 18 hours, you have a 24 hour window to claim that day's essence.
Some servers include essence streaks, which increases the amount of essence awarded per day if you maintain a login streak.
Some servers include additional essence in the daily award if you vote for the server on minecraft server lists.
Essence is primarily used in certain factory recipes, as well as upkeep for exile pearls.