The Hanukkah gift giving is a new concept that has evolved out of the Hanukkah gelt giving tradition. In the past times, Hanukkah gelt (Yiddish for "money") was distributed to children to enhance their enjoyment of the Hanukkah holiday. (The amount given was usually in small coins, although grandparents or other relatives may give larger sums as an official Hanukkah gift. In Israel, Hanukkah gelt is known as dmei Hanukkah. Many Hasidic Rebbes distribute coins to those who visit them during Hanukkah. Hasidic Jews consider this to be an auspicious blessing from the Rebbe, and a segulah for success.)
Since Hanukkah falls on the same time as Christmas, it has led to the expansion of the gelt giving tradition to gift giving tradition. There are many different things that one can buy to present as Hanukkah gifts such as a Hanukkah menorah, Hanukkah decorations or just year round productss such as Jewish books or ordinary Judaica. You might also want to give an exquisite Hanukkah gift baskets.