Passover (Pesach or פֶּסַח) is an annual celebration in the Jewish faith which falls on 14 Nissan, the first month of the Jewish year. It commemorates the escape of the ancient Jews from slavery in Egypt, which is often considered to mark the beginning of the Jews as a people. It is one of the most important holidays in the Jewish calendar and is one of the three pilgrimage festivals (the other two being Sukkot and Shavuot) on which everyone was expected to make pilgrimage to the Temple in Jerusalem. Passover has a variety of names, including 'The holiday of matzoh' (Chag HaMatzot) and 'holiday of our freedom.' (Zman Cheiruteinu)
The holiday is celebrated for seven days in Israel and eight in the rest of the world as during the Second Temple period the signal fires used to communicate the start of the new month (and thus when the holiday would fall) were frequently interfered with by the Samaritans seeking to disrupt the Jewish community. It is a holiday full of symbolism, of which the best known is the matzoh, or unleavened bread, eaten to remind us that we had to leave Egypt so quickly, we couldn't wait for bread to rise. (Matzoh is a little like an unusually tasteless cracker, and is the subject of a lot of jokes.)
The holiday begins with the lighting of the candles at sunset, followed by the evening (Ma'ariv) service at the synagogue. The highlight is the festive ceremonial meal called a seder, in which the escape from Egypt is recalled, and the participants are urged repeatedly to consider themselves as personally having escaped from slavery. This involves drinking four cups of wine and yelling about frogs, and concludes with the story of dad's poor little goat.
The solar calendar dates vary, since Judaism uses a combined solar-lunar calendar which keeps the holidays aligned with a specific season. (In contrast, the Muslim calendar is completely lunar so that holidays like Ramadan will occur in different seasons of the year.)
The Christian Easter holidays were originally based on the timing of Passover, since that was why Jesus was in Jerusalem. The Last Supper was a celebration of Passover. However, both the Western and Eastern churches long ago divorced the exact timing of their Easter observations from the Jewish celebration, in order to make them less "Jewish".