The Jews eat the Passover Seder meal on the night of Passover (Pesach). It makes little difference whether Passover begins on Shabbat or on a weekday. Note that there are festive meals on every Shabbat, but they are not called "seder" and the foods are different.
Generally it occurs only during Passover, a Jewish holiday. There is also a seder for the holiday of Tu Bishvat, but this seder is rarely observed.
you can NOT attend a seder meal
It symbolizez the bitterness of life in ancient Egypt for the Jews.
There is no prohibition against eating kosher meat during Shabbat. The reverse is true; it's expected that meat be eaten during the two main Shabbat meals. On Passover, Jews cannot eat leavened bread (whereas they can at other times of the year). Shabbat does not mirror this. The same kosher rules for the rest of the week apply on Shabbat. Jews cannot eat pork on any day of the week and conversely, Jews can eat tuna or kosher meat on any day of the week.
There is the Seder plate, or Keharoh, but no one eats off it. It is where all the symbolic food (according to some, not the matza) in placed.
People eat the Seder meal as part of the Passover celebration. It is a symbolic meal that commemorates and retells the story of the Israelites' liberation from slavery in Egypt, as instructed in the Torah. The meal follows a specific order outlined in the Haggadah, a text that guides the rituals and readings during Passover.
At the time of the Mishna (200 CE), rabbis deemed it meritorious to eat fish on the Sabbath and Jews became accustomed to eating fish at festive meals. Gefilte fish, which has been called the quintessential Jewish food, is an especially popular fish to serve at the Passover Seder meal.
They pray, eat, pray, and eat some more. And sit around and shmooze a lot.
It's not the meal that's so important. It's the telling of the Passover story, along with its symbolic foods (and then dinner) that is critical. The story of the liberation from Egyptian slavery is the central event in Judaism, and Jews are commanded to retell and relive the story every year, as though they themselves had been freed from slavery.
Jews eat the Passover meal to commemorate what happen to them a long time ago. In the Bible, it explains that the Jews were taken out of Egypt, in a hurry. Their bread did not have a chance to leaven, and so they ate what they call "matzoh" Now Jews have a meal with "matzoh" in it, to commemorate it.
This question likely comes from the differences in phrasing of the second question of "Ma Nishtana", the set of four Passover questions. The question is, "On all other nights we eat many vegetables, why on this night, [only] bitter herbs?". The word "only", put in brackets here, is inserted in some versions and removed in others. This is likely a problem deriving from remembering the questions of "Ma Nishtana" incorrectly, because the first question has a similar format: "On all other nights we eat both leavened and unleavened bread, why on this night, only unleaveaned bread?" Since the format was similar, the "only" in the first question, which is legitimate - no leavened products are eaten on Passover, it was incorrectly carried to the second question.As others have noted, Jews eat a variety of other vegetables on Passover, most notably the "karpas", which is a piece of parsley or celery that features in the Seder celebration. Additionally, most Jews will include some vegetables in the meal that is served during the meal-portion of the Seder. So, the premise behind the question of "only" is incorrect.
Most Jews call the Passover meal the Seder, a word which means "order," in reference to the order of service or liturgy of the meal. It is sometimes called the Feast of Freedom because it celebrates the liberation of Jews from slavery in Egypt. It is also sometimes called the Feast of Unleavened Bread because it features unleavened bread and one of the high points of the liturgy of the meal is the command to eat unleavened bread.