Chanukah is by Jewish religious standards a very minor holiday, whose importance in the United States has been magnified far beyond its historical significance merely because of its proximity to Christmas in the secular calendar. Due to the omnipresence of Santa Claus/Christmas in media, advertising, stores, etc., regarding the giving of presents to children whether they have any idea of what the holiday is really about or not (or even whether they care about that or not), it has become more or less traditional for less orthodox (especially Reformed) Jewish families to exchange gifts at Chanukah (despite the fact that there is absolutely no religious or historical basis for doing so) simply because otherwise Jewish children too young to understand that Christmas is a Christian religious celebration unrelated to our faith would be crushed by their failure to receive gifts in December while their Gentile friends receive a flood of gifts from Santa Claus. The problem arising was the identification of the deliverer of these gifts. Since Santa Claus is a figure associated with the Christian holiday, and thus unsuitable to be identified to Jewish children as the deliverer of the presents to be found under the Chanukah Bush (another modern American Jewish invention without religious or historical basis used in some Jewish homes to provide context to Jewish children too young to understand the situation), the Chanukah Birdie (a close relative, I suspect, of the stork who delivers babies) was invented to fill that imaginary role.
BTW, if you want an explanation of Orthodox, Conservative, Reformed, Liberal, and Reconstructionist Judaism, and the differences between them all (including all the shades of each), you're going to have to get that from my brother, the rabbi.