Ash Wednesday is the start of Lent. Lent is 40 days long, starts on Ash Wednesday and ends on Good Friday. Since Easter Sunday is a movable feast, Good Friday is also a movable feast, and therefore Ash Wednesday being exactly 40 days earlier, also has to be a movable day - not exactly a "feast day", since it is a day of fasting and abstinence.
On Ash Wednesday during Mass, the people all process up to the altar, and the priest makes the sign of the Cross on their foreheads, with his thumb which has been dipped in ashes.
The ashes are made by burning the left over Palms from Palm Sunday the year before.
In the Bible a mark on the forehead is a symbol of a person's ownership. The cross is a symbol of Jesus Christ who died on the cross, so this mark on the forehead signifies that the person is owned by Christ.
Ashes are a biblical symbol of mourning and penance. They are also a reminder of our mortality ("Thou art dust and unto dust thou shalt return").
So it is an appropriate substance to use for the beginning of a period of mourning and penance, leading up to Good Friday.
Ash Wednesday is not a Holy Day of Obligation, meaning that we do not HAVE to go to Mass, but it is a highly desirable Mass to attend, in order to receive the sign of Christ (cross of ashes on the forehead) and to recognise that Lent starts today!