The manifestation counter is a new type of counter in the new set, so until other cards that interact with manifestation counters are spoilered or Wizards introduces a new ruling that deals with manifestation counters (like how poison counter has a ruling that says a player with 10 of them loses the game), we can only guess.
Alright, so I guess at the moment its a really cool draw/cheating in ability.
The manifestation counter is currently only a visual reminder that the permanent is an enchantment in addition to its other types. That much can be assumed based on the ability that creates and distributes the counter.
We currently have no specific rules definition for manifestation counters, so we cannot presume what else they mean.