Today marks the first day of Lent, during which time Christians (mostly Catholics, Lutherans, Methodists, and Presbyterians) will fast, abstain from meat on Fridays, or simply do their best to refuse their earthly pleasure of choice. Of course, today is also known as Ash Wednesday, when worshippers attend services, start their fasting, and, most notably, wear ashes on their foreheads.
Since Lent represents the time that Jesus spent wandering in the wilderness, it's an understandably solemn time. While worshippers are encouraged to reflect upon their commitment to their faith and the community throughout the season, Ash Wednesday services place a special emphasis on mortality and sinfulness. That's where the actual ashes come in.
Depending on the Mass, ministers will either sprinkle ashes over worshippers' heads or use a blend of ash and holy water to rub the sign of the cross into their foreheads. The ashes themselves come from the palm leaves that were blessed during Palm Sunday (the Sunday before Easter) of the previous year. Usually, the minister will recite the following words while administering the ashes: "Remember that you are dust, and to dust you shall return."
As that exchange might suggest, the ashes represent the literal "dust" from which God made all people — and it's intended as a stark reminder of our own mortality. More generally, ashes have long been associated with sorrow, purification, and rebirth, which all play a role in the story of Easter Sunday (the end of Lent).
Tradition holds that Christians wear ashes on the first day of Lent in order to mourn and acknowledge the suffering that Jesus endured. As a gesture, it represents a willingness to repent for your sins and purify your soul in preparation for his resurrection.
Worshippers may wash off their ashes right after services or leave them on for the rest of the day. Traditionally, it's frowned upon to go out in public with your ashes on display, but nowadays it's pretty common to do so.
Even if you observe Lent, you aren't required to wear ashes. This time of year is already demanding for those Christians who choose to fast and abstain — donning ashes for a day (or even a few hours) is just another way to demonstrate devotion to the faith leading up to Easter.