It's not mentioned in the Bible. None of the apostles observed it. Nowhere are Christians commanded to keep it. It was not even officially practiced until nearly 1000 years after Christ's resurrection. Like so many other non-biblical 'Christian' customs, it has pagan roots. It's a sad fact that modern Christianity has appropriated so many customs from the practice of the heathens, that one might wonder if it should still be called Christianity.
This ritual 'imposition of the ashes' is purportedly in imitation of the repentant act of covering oneself in dust and ashes. The marking of believers on Ash Wednesday is done in combination with another extra-biblical tradition called 'Lent'. Despite Christ's command to his followers to abstain from the practice of disfiguring their faces during fasting, it has become a regular practice. He also told us to wash our faces during a fast.
The practice of putting ashes on one's forehead has been known from ancient times. In the Nordic pagan religion, placing ashes above one's brow was believed to ensure the protection of the Norse god, Odin. This practice spread to Europe during the Vikings conquests. This laying on of ashes was done on Wednesday, the day named for Odin, Odin's Day. Interestingly enough, according to Wikipedia, one of Odin's names is Ygg. The same is Norse for the word Ash. This name Ygg, closely resembles the Vedic name Agni in pronunciation.
The Norse practice which has become known as 'Ash Wednesday' was itself, drawn from the Vedic Indian religion. Ashes were believed to be the seed of Agni, the Indian fire god. It is from this name that the Latins used for fire, ignis. It is from this root word that the English language got the words, ignite, igneous and ignition. Agni was said to have the authority to forgive sins. Ashes were also believed to be symbolic for the purifying blood of the Vedic god Shiva, which it is said had the power to cleanse sins.