References to a “day of ashes” liturgy as the start of Lent can be found as early as the 8th Century. Ashes are an ancient part of repentance rituals, as mentioned several times in the Old Testament and practiced in other religions, as well. They were a sign of humbling oneself before God.
The ashes used in Christian liturgies traditionally are made by burning palms saved from the previous year's Palm Sunday liturgy. The officiant places his or her thumb in the finely ground ashes, and then makes the sign of the cross on the worshiper's forehead. The cross, of course, refers to Jesus. The words used in imposing ashes are, “Remember that you are dust, and to dust you shall return,” or some variant. Those words refer to the creation story, when God made humanity out of earth.
This ceremony has several layers of meaning. But the heart of it is accepting one's humanity, acknowledging God as creator, confessing one's sins, asking God for forgiveness, and pledging to go forward in “newness of life.”