Along with Easter, Christmas is one of the two holiest days in the Christian faith. The holiday, held on Dec. 25, marks the birth of Jesus Christ. According to the biblical story, Christ was born in a manger (a stable) beside an inn in Bethlehem, near Jerusalem. The birth was marked by a brilliant star (the Star of Bethlehem or the Christmas Star), which led three magi (wise men) to the stable with gifts of gold and the incenses frankincense and myrrh. Shepherds in a nearby field were visited by an angel, who announced the son of God had been born.
The holiday has become widely celebrated in a secular way in Western countries, including by non-Christians, with additions like Santa Claus and his reindeer, Christmas trees, and presents. Many of these additions bear some religious significance -- Santa Claus is actually based on a Turkish Christian saint named Nicholas who lived in the third century, and Christian reformist Martin Luther is credited with creating the tradition of decorating a tree for Christmas.
In the Christian faith, the holiday is meant to share good tidings and fellowship, so don't be surprised if you're invited to a Christmas party. There, you'll likely find a nativity scene recreating the manger at the time of Christ's birth. Secular adornments like garlands made of evergreen boughs may also adorn the home, and candles may be lit to reflect the stillness and comfort the night symbolizes.
While any small token of gratitude will make an appropriate gift for your hosts, you can also show respect for their religious beliefs. A Christian-themed carol book is a good present, and may get the party guests singing. If your host has a Christmas tree, a religious ornament for it is another great gift. And Christian-themed cookie cutters will get your hosts baking, while helping pass along their religious beliefs to their children.
Food is also always welcome. Gingerbread houses don't have any religious significance, but are an innocuous and well-regarded gift. The same goes for eggnog, although you may want to pass on bringing any alcohol to add to it, as your host may abstain out of religious observation.