Answer:
Depending on which holiday you are asking about and which part of China did they come from as well.
For example:
During Chinese New Years, we eat rice cakes. Northern Chinese would like eating dumplings (i.e, 金元寶 which some resemble ancient Chinese gold ingots). We also eat dishes with names that sounds pleasant, like fish (YU) where YU have similar pronunciation as 'excessive', 'surplus', etc.
In Mid-Autumn Festival or Lantern Festival, we eat mooncake.
For Tuen Ng/Duanwu/Dragonboat Festival, we make these rice dumpling called zongzi that are usually wrapped in banana leaves. (There's an ancient story why we made this)