What does it mean when you have this type of card?

If you are playing this house and have something out of house, can you use that something on the out of house "X"

From the rule book:

"Your plot deck and your House deck may not contain any card that contains the words 'House X only' unless House X is the House you are playing (i.e., the House denoted on your House card)."

For example, if you build a deck with the Lannister House card, you can have as many "House Lannister only" cards in it as you want. But you cannot have any "House Greyjoy only" cards in it at all -- no matter what card type, House affiliation, etc. that "House Greyjoy only" card might be, and not even if you are playing an Agenda that would allow you to ignore OOH gold penalties on Greyjoy cards.

You can have them only if you have an agenda (only an agenda would allow that) that specifically states you can have "House X only" cards for houses other than your own. So far, only one exists: City of Shadows.

Also if you delve into the draft format of the game. The agenda allows you to use house X only cards as well but you need 5 more power.

Cheers,