What does "played from your hand" actually mean?
This is old wording. You may check the Gatherer for the most recent wording of cards. Currently that Myojin's gatherer text says the following instead:


  Myojin of Cleansing Fire enters the battlefield with a divinity counter on it if you cast it from your hand.


"Cast from your hand" means you took it from your hand, cast it onto the stack, and then it entered the battlefield.

This is as opposed to:


simply being put onto the battlefield without being cast (e.g. via Champion of Rhonas)
being returned from your graveyard to the battlefield (Rescue from the Underworld)
being cast from a zone other than your own hand:


from the graveyard (Havengul Lich)
from exile (Daxos of Meletis)
from your library (Vizier of the Menagerie)
from the command zone in a game of Commander
from someone else's hand (Desertion or Sen Triplets).