Burnt offerings were made voluntarily, and seem to have been the most common type of sacrifice (cf. Ex. 29:38-43). They purified a worshiper from general sin and thus prepared him to draw near to God. This offering was completely burned up to show that it was completely dedicated to the Lord.
To "make atonement" [(Lev.) v.4] meant that the animal died a substitutionary death in place of a worshiper. By laying hands on it, worshipers showed an understanding of sin and a repentant heart. We know that the blood of these animals did not actually remove sin - only the blood of Christ can do that-but the sacrifices did purify people outwardly and make it possible for them to be in the presence of God (Heb. 9:11-14).
Today in the Word, p.6