The Mitzva of Para Aduma is a חוק, a Mitzva that no reason is given for it. Some Meforshim say that the cow acts as a redemtion for the cow that was made in the desert. Just like the Bnai Yisrael were so quick to get all of their riches in order to make the golden calf, so too by the Para Aduma, the Bnai Yisrael have to pay for it through their own money.
Before the sin of the golden calf, the Bnai Yisrael were whole and flawless, and afterwards they were filled with sin. The Para Aduma made Bnai Yisrael whole and flawless one again.
The Para Aduma was burnt together with cedar wood, some scarlet thread, and a hyssop. These three items represent the three thousand men that were killed because of the sin of the golden calf. The cedar tree is the highest of all the trees, and the hyssop is the lowest. This shows that when somebody sinned because he felt that he was much higher than everyone else, he was sprinkled with ashes of a hyssop, the smallest and modest of all plants. The ashes were preserved forever, just like the participants in the Cheit Haegel were never forgiven.