Bedrock

Bedrock is the block that makes up the very bottom of the world, preventing access to the Void. It has an 18,000,000 blast resistance, making it the hardest material in the game. Bedrock cannot be broken in Survival Mode without the help of editors.

Mining
Bedrock may be broken on Update 0.11.0 or earlier in Survival mode if the player makes a large enough space and activates the Nether Reactor on the last bedrock layer. However, because the Nether Reactor was removed in Update 0.12.1, this is now impossible without modifying the game.

Trivia

 * Invisible Bedrock makes up the sides of Old worlds, preventing players from falling off the edge of the world. It is possible to place Ladders, Fences, Torches,etc. on it.
 * The bedrock resists TNT explosions, so it could be used to make cannons.
 * You can break bedrock in Creative Mode.
 * After 0.12.1 came out, there is now no way to break bedrock in Survival. Since the Nether Reactor was removed, it's impossible without a mod or something similar.
 * A while ago, there were some bedrock clouds in the seed "jp gaming", most likely from a Herobrine glitch.