I am wondering what the military part in bold is referring to on this card. I have always played it that I can make any one challenge. Is this correct

What type of card is this? For which house?

This is a Plot Card

http://www.agotcards.org/card/v/4206

"Military Battle You cannot declare more than 1 challenge. You cannot declare defenders. This plot's text cannot be blanked."

"Military Battle" is a Trait . It does nothing by itself, but there are other cards that can interact with it (At the Point of a Blade, The Lion's Law, etc). It does not affect what kind of challenge you can declare.