It was the Yule Ball, and you were one of the four champions date. Your arm was interlinked, since you and your date had to walk in first, due to them being a champion.

Dumbledore: “Now, here we have our four champion’s! Fleur Delacour, Viktor Krum, Cedric Diggory, and Harry Potter!” he announced, the four walking through the parted crowd with their dates and onto the dance floor..they were the ones having the first dance..