What exactly does the Hidden keyword do?

Ruling: You pay one power to set a unit hidden to a battlefield you control. Starting next turn, you can play the card for free as a reaction, with the restriction that it only affects the battlefield it's been placed on.

Sequence:

• Step 1: Pay one power to set the unit hidden to a battlefield you control
• Step 2: Starting next turn, you can play the card for free as a reaction

Nuances:

• The card can only affect the battlefield it's been placed on
• You ignore the casting cost when playing it from hidden