A gift (or money) given to someone who has moved house to celebrate their new home; a housewarming present.
友人の引越し祝いに食器セットを贈った。
I gave a set of dishes as a housewarming gift to a friend.
引越し祝いは現金より実用品を贈ることが多い地域もある。
In some areas people prefer practical gifts over cash for housewarming presents.
新居に招かれたら引越し祝いを持って行くのが礼儀だ。
If you're invited to someone's new home, it's polite to bring a housewarming gift.