In Sonic the Hedgehog 4: Episode 1 for the PS3, Xbox 360, Wii, and iPhone/iPad, each level has a bonus stage that you can access. These bonus stages are where the Chaos Emeralds located.
To access any levels bonus stage, you need to collect 50 rings in that level. Once you do, a giant ring will appear at the end of the level. Jump into the ring and you’ll be taken to the bonus stage for that level. Once you collect the Chaos Emerald for that stage, the bonus level will no longer be accessible.