During the reading of the Haggadah (the story of the exodus from Egypt), we eat a number of symbolic foods. We dip a couple items into salt water, the salt water represents the tears of slavery.
Salt water
life
You do not dip anything on Purim. You are referring to the holiday of Passover, and the vegeteble is called Karpas (כרפס)
well it depends on the kind of dip
Eggs, they also eat unleavened bread (bread without yeast)
juicy foods
Breadsticks
The Passover (Pesach) Seder is a special festive meal held on the night of Passover. In it, Jews tell of the Exodus (From a book called the Haggadah) and have specified foods (including matzoh and bitter herb).
They have to shop for Kosher for Passover foods and clean their homes of ALL regular bread and bread products.
As soon a passover ends, leavened foods are again permissible, subject to other general kosher laws.
Dip in liquid
Dip