On Passover, bread is replaced with matza, an "unleavened bread" made from flour and water with no yeast. The flour itself is carefully watched that no fermentation should have started before it is made into matza. Hundreds of years ago, matza was only eaten dry. While it could be used for sandwiches, it could not be soaked in water to become an ingredient in other foods. Then a great Rabbi ruled that it was OK to soak the matza in water since no fermentation could take place once it had been baked. The matza ball or Knaidle was promptly invented, and today it just isn't Passover without chicken soup with matza balls (knaidlach).
You can follow the recipe on the matza meal box, or try this one, which I learned in Israel: Ingredient List:
SET it on stove to boil
PUT fat or oil in a medium saucepan
ADD onion and carrot and heat until soft & wilted
ADD the cup of water and bring to boil
ADD the matza meal all at once and stir to mix.
REMOVE from heat. It will be very thick.
ADD the eggs and mix. You can do this in the same pot, or put it all together in a bowl.
ADD the parsley and mix.
When the water in the big pot is boiling, make balls of the matza meal mixture, dipping your hands in some cold water between each ball, so it will be smooth and not stick to your hands. If the mix is too soft to easily roll the balls, add some more matza meal.
Makes 30 balls about 1-1/2 inches across
Put each ball directly in the boiling water, as you make it, and they will rise to the top as they are done.
Add the balls to hot soup, and eat.
(Some people prefer to cook their matza balls right in the soup, which is OK if you have lots of soup since the balls do absorb some of it while cooking.)