What does Hebrews 10:4 mean?

This verse states, directly, what the writer of Hebrews has been implying for several chapters. The animal sacrifices offered by the priests of the Old Testament had to be repeated often (Hebrews 9:6–7). Logically, this means those sacrifices were not actually obtaining forgiveness for sins; they were only covering up those sins, temporarily delaying judgment. Through many quotations in the Old Testament, however, the writer has shown that this was always God's intention. The old covenant was meant to symbolize the new covenant, to prepare mankind to accept the ministry of Jesus Christ. The very flaws which have been pointed out, in fact, were meant to draw mankind's awareness to our need for a single, perfect sacrifice (Hebrews 9:8–10).

In the prior chapter, it was mentioned that animal sacrifice can assuage feelings of guilt, but cannot truly change the conscience. In this context, this means animal blood can only solve a ceremonial problem: something physical and external. Our real problem with sin, however, is internal. This is why God promised to establish a "new covenant" written on the hearts and minds of the people.