Lord Shiva is usually depicted as sitting or meditating on a tiger skin. Lord Shiva is usually portrayed as wearing a tiger skin as garment. Tiger symbolically represents power. Shiva sitting on tiger skin and wearing it symbolically means that He is beyond all power and dominates over all the powers. There is an interesting story in the Shiva Purana which narrates about how Lord Shiva got the tiger skin.
Once Lord Shiva was roaming around the world like an Avadhuta. He was completely naked and was so merged in this meditation that he was unaware of any other existence.
During His roaming, once He reached a forest inhabited by a group of saints.
The saints became furious after they realized that it is the new mendicant that is responsible for the wayward behavior of the females in their society.
The saints decided to teach the young mendicant a lesson and dug a pit on his usual way. When Lord Shiva passed over the pit, the saints created a tiger using their powers.
Lord Shiva easily overpowered the tiger and removed its skin and made a cloth out of it.
The saints realized that the mendicant was no ordinary Avadhuta and prayed for forgiveness. Lord Shiva appeared before them and blessed them. From that day onwards Shiva started wearing the tiger skin.