The quest to make it to The End in Minecraft is certainly an epic one. Players have to go to the depths of the overworld in order to find diamonds, mine solid blocks of obsidian, traverse the perilous fields of lava in the Nether, hunt down the formidable Endermen mobs, find a hidden stronghold buried deep underground, and then finally they come face to face with the Ender Dragon itself. This fight is challenging as well, but players that manage to beat it are awarded with a ton of experience and a Dragon Egg. Despite their best efforts, players haven't figured out how to hatch this egg yet.
Of note, the Dragon Egg is the single most rare item in all of Minecraft, as it can only be obtained once. After killing the Ender Dragon and getting the egg, there is no way to spawn another egg without using cheats such as the /give command. It doesn't even appear in the creative mode menu in Minecraft, and is the only item missing from that list.
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The short and simple of it is that vanilla Minecraft players cannot hatch the Dragon Egg. There's simply no feature in the game that would allow the player to do this. Instead, the Ender Dragon Egg serves as a trophy of sorts, proof that the player managed to defeat the Ender Dragon. If players want to actually hatch the egg, they will need to install mods that allow them to do so, as this is not something that is possible in vanilla Minecraft.
The Ender Dragon can be respawned, but this doesn't involve hatching a new one. Instead, players can respawn the Ender Dragon by making four End Crystals and placing them on the End Portal. Keep in mind that killing a second Ender Dragon will not result in another Dragon Egg spawning, as this only happens the first time.
There are a lot of great mods that players can use to make their Ender Dragon hatchable, although these will only work with the PC version of Minecraft. Some of them add baby Ender Dragon models into the game, others hatch full grown Ender Dragons but allow the player to control or even ride them. It's possible that Minecraft will make the Dragon Egg hatchable some day in Bedrock Edition, but it will likely be a while. Part two of the Caves and Cliffs update releases later this year, so the next major yearly update would be the earliest. Perhaps if Mojang opts to overhaul The End just like it did the Nether this may become a reality.
Minecraft is available now on Mobile, PC, PS4, Switch, and Xbox One.