The Book of ויקרא deals heavily with קרבנות. Rabbeinu Bechaye noted some interesting characteristics of some of the animals fit for sacrifices.
One common factor of appropriate animals is that they are נרדפים, chased as prey by other animals. They do not attack or consume other animals.
The תורים, turtle doves were worthy of sacrifices because they were very loyal animals. The females would never mate with another turtle dove once it had already mated.
We learn that parts of the fowl were, nevertheless removed before being offered. This was because the bird most likely found its food by way of גזל, stealing. And stealing was considered one of the worst human flaws.
There is great significance and symbolism related to the קרבנות. What is most important is the כוונה, or intent in how it is offered. Proper כוונה is what allows the קרבן to achieve its ultimate purpose.