When a Jew needed to bring a korban, he would try very hard to give the best of his animals to HaShem. Even though it would be cheaper to sacrifice a weak or small sheep, for example, he would try his best to offer the fattest, healthiest sheep he could afford. In this way, a person would elevate and beautify the mitzvah, by doing it in the best possible way. In the same way, we try to do all of the mitzvot in as beautiful a way as possible- we buy the nicest etrog we can afford on Sukkot, and the highest quality tefillin and mezuzot, Parents pay tuition to Jewish day schools so that their children will have the best possible education.
Of course, if a person could not afford expensive korbanot, he could offer less expensive ones, and still fulfill the mitzvah. As long as he had the proper intentions, HaShem accepts his offering wholeheartedly.
Korban Olah - The Animal Offering
There are several kinds of korbanot, each with its own special purpose.
A Korban Olah is a very holy type of sacrifice that is burned completely on the altar. Olah means to go up. The whole animal "goes up" to HaShem; nothing is left over for the owners or for the Kohanim.
A person voluntarily chooses to offer an Olah, and brings the animal to the Mizbeyach (altar) in the Mishkan, where the Kohanim burn it.
The ideal kind of Olah offering is a male animal - either a bull or ram or goat. But these large animals are expensive, and usually wealthy people are the only ones who can afford to give big animals as a Korban Olah. A somewhat less well-to-do person might give a smaller animal.
Or, if a person wants to bring an Olah, but can't afford to give an animal at all, he can give a bird instead. He has two kinds of peaceful, kosher birds to choose from: a pigeon or a turtledove.
Korban Minchah - The Flour Offering
If someone is too poor to offer even a bird, then he can still fulfill the mitzvah of bringing an Olah by offering a sacrifice of dough made from flour, oil, and spices. The dough can be raw, fried, or baked - as long as it doesn't rise. This type of Olah is called Minchah, which means "gift."
To bring a Korban Minchah, the person gives the dough to the Kohein, who takes a handful in his fist, brushes off any excess with his thumb and pinky, sprinkles salt and spices on it, and then burns it on the Mizbeyach. The rest of the dough is given to the Kohanim to eat.
The Minchah offering given by a poor person is very precious to HaShem. Even though it doesn't cost much, to the person who had to give it up, it was valuable. Perhaps sacrificing flour and oil meant the person couldn't bake bread for himself, or even that he had to go without food. To HaShem, the humble Minchah is His favorite, because since he sacrificed his own needs in order to bring it, it is as if the poor person has offered his nefesh "his very own life" on the Mizbeyach.
Korban Shlaimim - The Peace Offering
Since a person who brings an Olah or Mincha offering doesn't eat any of it, he might sometimes also like to bring another kind of sacrifice, called a Korban Shlaimim, or peace offering. With a Shlaimim, a person who is feeling grateful for the good things he has can serve HaShem with a sacrifice expressing his happiness and thanks. At the same time, he can celebrate and eat with friends and family, and share the cooked meat from the sacrifice with the Kohanim.
For a Shlaimim, a person can bring an ox or cow, ram or sheep, or male or female goat. He brings the animal to the Mizbeyach, rests his hands on the animal's head, and says special words of thanks to HaShem before the animal is offered on the altar.
The word Shlaimim comes from the root of the word Shalom, which means "peace." Since the meat is shared with other people in a spirit of happiness, this type of korban helps create a feeling of friendship and peace among people. It's the same feeling you get when you sit down to a meal with family and friends on a special occasion.
