In the wartime world of the play, honour is important.
Prince Hal is the first born son of Henry IV and therefore he knows that he will one day be king. He knows his duty which includes a code of honour. For the moment, he is content to sow his wild oats. He speaks of all of this in Act I, scene 3 in a soliloquy at the end of the scene. Does he want to be king? "So when this loose behaviour I throw off/And pay the debt I never promised,..." It doesn't sounds like he does, at least at this point in his journey.
Hotspur as his name implies is hot tempered. His honour will not permit him to give his prisoners to the king. In fact, in Hotspur's world the king is not an honourable man. If it had not been for Hotspur, his father the Earl of Northumberland and the Earl of Worcester, Henry would not be King Henry IV. Their support in their opinion was honourable whereas Henry proved to be dishhonourable.
Falstaff is the realist about honour. He speaks about it at the end of Act V, scene 1. For him, honour is just a word that has no practical application. It can't mend a broken arm or leg. It can't perform surgery or take away pain or grief. The dead have honour not the living. It has no senses. He concludes that, "Honour is a mere scutcheon" and tells us he wants nothing to do with it.
Each man holds a different view of honour with Hotspur and Falstaff representing the extremes. For Prince Hal, it is part of his duty as the future king and when the time comes he behaves honourably.