The word Yalda derives from a Syriac word meaning birth (compare the Arabic word "yeled" meaning "young boy"). According to Wikipedia, it was Syriac-speaking Christians who brought the word to Iran during the Sassanid period, where the coincidence of Christmas (the celebration of the infant Jesus) with the time of the Winter Solstice, more or less, led to the use of this word for the Winter Solstice festival in Iran. You can read more about the ancient Zoroastrian roots of this festival at FarsiNet.
Some of the traditional foods associated with the Yalda night celebrations are pomegranates and watermelons. Here is a picture of special items for this Iranian winter feast, and you can read about this year's Yalda in the world news using this Google News: Yalda search.