Purana

In the Hindu epics

The first elaborate account of Kartikeya's origin occurs in the Mahabharata. In a complicated story, he is said to have been born from Agni and his wife after the latter impersonated the six of the seven wives of the 'Seven Sages'.The actual wives then become the Pleiades. Kartikeya is said to have been born to destroy the Asura Mahisha.(In latter mythology, Mahisha became the adversary of Durga. Indra attacks Kartikeya as he see the latter as a threat, until Shiva intervenes and makes Kartikeya the commander-in-chief of the army of the Devas. He is also married to Devasena, Indra's daughter. The origin of this marriage lies probably in the punning of 'Deva-sena-pati'.It can mean either lord of Devasena or Lord of the army(sena) of Devas.
The Ramayana version is closer to the stories told in the Puranas discussed below.

In the Puranas

Though slightly varying versions occur in the Puranas, they broadly follow the same pattern. (By this period, the identification of Shiva/Rudra with Agni, that can be traced back to the Vedas and Brahmanas, had clearly made Kartikeya the son of Shiva.)
The Skanda Purana narrates that Shiva, was married earlier to Dakshayani( also known as Sati), the granddaughter of Brahma, and the daughter of Daksha. Daksha never liked Shiva (Shiva begs for food, lives in a graveyard covered with ashes being the Destructor, and has no possessions, not even good clothes for himself - symbolising detachment but disliked by Daksha) and insults Shiva in front of Dakshayini in a Yagna. Dakshayani self-immolates herself, unable to bear the humiliation. Having thus incurred Shiva's wrath, the Yagna is destroyed even though it was protected by all the other Gods & Rishis. Taraka believed that, since Shiva was an ascetic and his earlier marriage was itself conducted with great difficulty, his remarriage was out of the question, hence his boon of being killed by Shiva's son alone would give him invincibility.
The Devas manage to get Shiva married to Parvati (who was Dakshayani, reborn) by having Manmatha (also known as Kama), the god of love awaken him from his penance, incurring his wrath by opening his third eye of destruction, and being destroyed & resurrected. Shiva hands over his effulgence of the third eye used to destroy Manmatha to Agni, as he alone is capable of handling it till it becomes the desired offspring. But even Agni, tortured by its heat, hands it over to Ganga who in turn deposits it in a lake in a forest of reeds(Shara). The child is finally born in this forest(vana) with six faces-eesanam, sathpurusham, vamadevam, agoram, sathyojatham and adhomugam. He is first spotted and cared for by six women reprsenting the Pleiades - Kritika in Sanskrit. He thus gets named Kartikeya. As a young lad, he destroys Taraka. As this youthful saviour he is called Kumara(the Sanskrit word for youth).