The circumstances leading the marriage of Shiva and Parvati is a significant episode in the Hindu mythology.
After the death of his first wife Sati, Shiva withdrew into an ascetic lifestyle, deep meditation and austerities.
Taking advantage of this, Tarakasura, the demon king secures an cleaver boon from Brahma, the creator. According to the boon, none could kill Tarakasura other than the son of Lord Shiva. Believing himself immortal, Tarakasura terrorised the universe and the heavens. Gods came to the verge of annihilation.
The only remedy, having a son born to Lord Shiva seemed impossible.
In the meantime Sati, Shiva's deceased wife reincarnated as Parvati. She was born to the Himavan, the god of the Himalayas and his wife the apsara Mena. She underwent severe austerities to impress Shiva to marry her.
The gods, in their desperation pursued Kamadeva, the god of love to disturb Shiva's meditation. Kamadeva succeeds but getting burned into ash in Shiva's fury. A lot many events later the Shiva-Parvati marriage finally materialises. Lord Brahma officiates the marriage.
Kartikeya was born to the Shiva-Parvathi couple who is considered as the 'god of war'. The second child born to the couple is Ganesh, the elephant headed 'god of the beginnings'. Kartikeya subsequently slew Tarakasura and bring peace to the kingdom of gods.
The marriage is a very popular theme in indian sculpture and temple art. You can also see playful mood of the couples in the Shiva-Parvati panel.