Yes, the significance of food does change in particular environments or on special occasions, within Judaism. Here are a few examples:
For the Passover meal, to commemorate Israel coming out of Egypt, foods such as unleavened bread is eaten. This symbolizes the Israelites fleeing Egypt quickly - they had to eat fast and they did not have time to wait for yeast breads to rise. Therefore, they ate unleavened bread. At Passover, lamb is eaten as well, this symbolizes "a sacrifice" - the shedding of blood from the animal, symbolic of paying the penalty for sins. This foreshadows Jesus Christ's sacrifice - the shedding of his blood on the cross.
Days of Unleavened Bread:
During these days each year, those who follow the Holy Days instituted by God do not eat any leavened products for a period of seven days. Leviticus 23:6 shows this in the Old Testament and the apostles kept this Feast in their day as well:
Old Testament - Leviticus 23:6 -"On the fifteenth day of that month the LORD's Festival of Unleavened Bread begins; for seven days you must eat bread made without yeast." (New International Version (NIV))
New Testament - "Therefore let us keep the feast, not with old leaven, nor with the leaven of malice and wickedness, but with the unleavened bread of sincerity and truth." (1 Corinthians 5:8).
The Days of Unleavened Bread represent putting sin out of our lives - not being 'puffed up' or leavened with sin.
Day of Atonement
A fast day, where the absence of food and drink - fasting - helps one draw closer to God. In the verse below, denying means to refrain from eating and drinking from sunset to sunset - a full day.
"The tenth day of this seventh month is the Day of Atonement. Hold a sacred assembly and deny yourselves, and present a food offering to the LORD." (Leviticus 23:27, NIV)