Always an offering should be without blemishes. We are told, by this, to give our best to the Lord. This is a peace offering, "instilling peace into the world." In order for this to happen, a portion of the sacrifice goes to the altar, a portion to the Kohanim (priest), and a portion to the owner.
I read this as a process of removing one's self from their daily tasks and concentrating their energies toward this higher ideal. It seems it would "work" to the extent that one would fully engage in the process. This process would begin in realizing the importance in such an offering and then in seeing what one could give.
I was once told that when you give art for a benefit, you should give your best piece. This seems to be an extension of the idea of giving an unblemished animal or pure ground flour.