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The story goes like this. While in the mount Mandhara a baby was born to Parvati and Shiva. Shiva was in a meditating posture and Parvati closed his eyes mischievously from behind. The boy appeared out of Parvati's sweat. Shiva explains to Parvati that since his eyes were closed, the baby was born blind and calls him Andhaka (the blind). Since he posed devilish qualities he was called Andhakasura (the blind demon ).

Hiranyaksha , a troublesome demon did intense penance to please Lord Shiva. Hiranyaksha wanted a son who posses immense powers to rule the world. Shiva refused to grant such a boon. Instead he offered Andhaka to Hiranyaksha saying that Andhaka posses all the qualities he was looking for , and to treat him as his son.

Andhaka wanted more power and did intense penance to please Lord Brahma (the lord of creation). Among many things, the boons he asked for included extraordinary vision and immortality. Everything was granted except the immortality.
Instead Lord Brahma asked him to choose when he could die. Andhakasura asked for a boon that he would die  only when he aspires for a woman who he should never aspire for.

With time Andhakasura turned more materialistic and less interested in austerities. By this time he has already conquered the world and the heaven.

On a pleasure trip he along with his companions lands up in Mount Mandara where Lord Shiva and Parvati lives.  His companions tells of a yogi and his beautiful wife. Andhaka sends his companions to bring her along. Shiva explains to them that they are Andhaka's parents. The companions mistook it for a ploy and compels Andhaka for a fight.
Shiva was in the middle of an austerity and the Andakha enters in a fierce battle with Veeraka, the guard of Shiva. The battle continued for many thousands years. And finally Shiva himself enters into the battle after he has completed the austerity.

Shiva stabbed Andhaka with his trident and held him high in the sky for 1000 years. Andhaka finally understood that Shiva and Parvati were his parents. Hanging on Shiva's trident, Andhaka praises Shiva's 108 aspects. And finally Lord Shiva touches his son for the first time. Andhaka became bright and luminous on the touch. He begs for and gets forgiveness from Shiva and Parvati.

The Shiva stabbing Andhaka is a very animated theme that adorns many Shiva temples. You can see this in either in the form of Andhaka hanging from Shiva's trident held up in the sky or Andhaka submitting under Shiva's feet.
You can see this is mythical theme Pattadakal and also in other famous ancient temples of Ellora, Elephanta, Belur, Somnathpur etc.

On a very similar note many temples have the image of Shakti ( consort of Shiva ) slaying the Mahishasura, the Buffello Demon. That's another mythical story anyway.