James Akin has a great explanation to the purpose of Ash Wednesday. Here is an excerpt:
Q: Why is it called Ash Wednesday?
A: Actually, Ash Wednesday is its colloquial name. Its official name is the Day of Ashes. It is called Ash Wednesday because, being forty days before Good Friday, it always falls on a Wednesday and it is called Ash Wednesday because on that day at church the faithful have their foreheads marked with ashes in the shape of a cross.
Q: Why do they have their foreheads marked with a cross?
A: Because in the Bible a mark on the forehead is a symbol of a person’s ownership. By having their foreheads marked with the sign of a cross, this symbolizes that the person belongs to Jesus Christ, who died on a Cross.
This is in imitation of the spiritual mark or seal that is put on a Christian in baptism, when he is delivered from slavery to sin and the devil and made a slave of righteousness and Christ (Rom. 6:3-18).
It is also in imitation of the way the righteousness are described in the book of Revelation, where we read of the servants of God (the Christian faithful, as symbolized by the 144,000 male virgins):
“Do not harm the earth or the sea or the trees, till we have sealed the servants of our God upon their foreheads.” (Revelation 7:3)
Q: Why is the signing done with ashes?
A: Because ashes are a biblical symbol of mourning and penance. In Bible times the custom was to fast, wear sackcloth, sit in dust and ashes, and put dust and ashes on one’s head. While we no longer normally wear sackcloth or sit in dust and ashes, the customs of fasting and putting ashes on one’s forehead as a sign of mourning and penance have survived to this day. These are two of the key distinctives of Lent.