Good question, since Bahá'ís do celebrate with gifts and parties, acts of charity and community service, and general good cheer. However, Christmas--literally, a mass for Christ--is at it's heart a holy day.
Ayyám-i-Há--the Intercalary Days--are those four (five in leap year) days left over in a solar calendar of 19 months of 19 days each. These are not 'holy' of themselves, but there is more to them than just parties and gift giving.
Bahá'u'lláh, Prophet-Founder of the Bahá'í Faith, instructed: Let the days in excess of the months be placed before the month of fasting. We have ordained that these, amid all nights and days, shall be the manifestations of the letter Há, and thus they have not been bounded by the limits of the year and its months. It behoveth the people of Bahá, throughout these days, to provide good cheer for themselves, their kindred and, beyond them, the poor and needy, and with joy and exultation to hail and glorify their Lord, to sing His praise and magnify His Name; and when they end--these days of giving that precede the season of restraint--let them enter upon the Fast. Thus hath it been ordained by Him Who is the Lord of all mankind. -The Kitab-i-Aqdas, p. 25
Note how He contrasts the days of giving with the season of restraint, the Fast. Ayyám-i-Há for me is a wake up call, a pause in the rush of my daily material life to help me remember and focus on the detachment from material things which will be needed during the Fast, and for my spiritual development in general.
Ayyám-i-Há is a Persian (Farsi) phrase that translates to Days of Há, and the choice of name has some hefty theology behind it, according to an interesting essay by Karla Jamir. Há is the Arabic letter corresponding to the English H, and is also the first letter of an Arabic pronoun commonly used to refer to God, or the Divine Essence. Há by itself is used as a symbol for the Essence of God, and is the subject of many religious essays on its mysteries. In the quote above, Bahá'u'lláh refers to the realm "beyond which there is no passing"--the realm of the Divine Essence--as Háhut.
So when Bahá'u'lláh designated the Intercalary Days amid all the nights and days as manifestations of the letter Há, He meant as Days of the Divine Essence. These extra days stand apart from the ordinary cycle of weeks and months and the human measure of time. They are not bounded by the limits of the year and its months--just as the infinite reality of the divine Essence of God is unbounded and cannot be captured or comprehended within the cycle of time or any other human measurement.
Thus Ayyám-i-Há can be thought of as days outside of time, days that symbolize eternity, infinity, and the mystery and unknowable Essence of God Himself. Contemplation during these days of the timeless mystery of the Essence of God provides us the joy and exultation with which to sing His praise and magnify His Name.