There are many holy days in the Jewish religion, some major and some minor. Because Judaism is fragmented into many groups and even cultures, not all of the minor ones are observed by all segments of Judaism.
The most important holy day in Judaism is the Sabbath,which begins at sunset on Friday evening, and which lasts until sunset Saturday evening. (In fact, all Jewish holy days begin at sunset.) The Sabbath is central to Judaism, no matter what segment of Judaism one is considering.
The Jewish new year, Rosh Hashona, and the day of atonement, Yom Kippur, which follows shortly after, are major Jewish holy days. Because the Jewish calendar is very different from the calendar we use for everyday life, these holidays fall on different days each year, but they always occur in the fall. Rosh Hashona is a joyous holiday, but Yom Kippur, being a day to atone and to fast, is more somber.
Another major Jewish holy day is Passover, known as Pesach. This is a spring holiday. This holiday is to celebrate the Jews' freedom from enslavement by the Egyptians, as Moses led them out of Egypt and got them on their way to the Promised Land. During a dinner called a Seder, the story of the enslavement and the flight from Egypt is told through a lengthy series of rituals, tales, and prayers. It's a lovely holiday, but it makes for a very long dinner!
Hanukkah, which is really a rather minor holiday, is celebrated in the winter, usually right around the same time as Christmas. It's meant to commemorate a famous battle and to celebrate a miracle following the battle. It seems to have become a more important holiday for Jews because Jewish children, who always get gifts on Hanukkah, don't feel so left out when Christmas comes around for their Christian friends. But the holidays really have nothing to do with one another.
There are so many more holy days, more than I can list in this space. I have included a link to a calendar that lists some of the holidays, so you can see there are many more. I have also included a link that can give you more details about some of these holidays. It is so interesting to learn about the holy days of other religions. I always love learning more myself.