Skeletron is a boss which can be 'summoned' by talking to the Old Man in front of a Dungeon at night. If you choose 'curse' when talking to him, he will immediately transform into Skeletron and start attacking you, so be prepared when this happens. This is a difficult boss, do not try to fight him unless you have lots of potions, good pre-hard mode equipment and/or throwable objects. It is also notable that Skeletron is the only boss that can only be summoned and defeated once per world.
In Ccoobbaallttmmaanns opinoin, defeating Skeletron with a Mining Helmet, Molten Breastplate and Molten Greaves, Spectre Boots, Grappling Hook with 15' hearts 'and a Dark Lance is actually really easy if you just run around grapple, and use your rocket boots and aim for Skeletrons closests body part. If you need more help, wacth the video.
Skeletron drops 5-10 Lesser Healing potions. While that is it, by killing him gives you acsses to the Dungeon.
Credit to hero for the video.