The Dragon egg was added in the beta 1.9 Pre-Release 5. It is an egg that is found and obtainable after defeating the Enderdragon. Clicking on the egg can cause it to teleport to a nearby area (up to five blocks vertically and fifteen blocks horizontally), creating the particles seen around Endermen and Nether Portals. Dragon eggs are like sand and gravel, they fall when unsupported. Since they aren't opaque blocks, they cannot suffocate the player. To collect it you can: move the dragon egg with a piston; trap the egg with bedrock then mine it; or trap with bedrock, place a non-solid block (torch works) under the block under the egg then mine the block under the egg, the egg should fall onto the torch and switch to item form.
It can be used as a monument to say you have defeated the Enderdragon in multiplayer, or as a golf ball, resulting in an extremely challenging game of golf. But in single-player, this has no use and the portal just leads to the MinecraftCredits.