Moving Zone is a new mechanic that associated with Air type monsters. This effect often describe as this sentence: 'Once per turn, this card can move to an unoccupied Monster Card Zone. When it did so, it can...'. It's like you can Moving them into anther column to UNLOCK their effects. Their effects are often weaken opponent's monsters, deal damage to opponent's LP or getting control the field. The main factor for them to work fluently is that they need SPACE to moving into another column. Then, when there are full cards in your monster card zone, you can't active this effect, to date only Zedra, King of the Speed is allowed to refuse that.
Also, a stronger monsters need more time to active their effect, by placing Storm Counter, and their effects are extremely powerful.