Minecraft is basically...uh..minecrafting. A random world is generated and you are dropped into it to survive. You do this by digging up the earth and harvesting plants and then crafting them into successively cooler stuff in order to give you a survival chance against the weird creatures that populate the world and tend to come out at night to fuck your shit up. You can also opt to turn off the weird creatures and just simply explore and dig and build without any threats (other than hurting yourself by falling). That's the basic summary. Most of the videos you see on YouTube where the person built something huge and insane were done in the old version of Minecraft where you could simply generate bricks out of thin air without having to craft or dig.
Pre-beta sandbox game! Everything is made of blocks! You break the blocks! You make things with the blocks! There are monsters made of blocks! No one knows why it is fun.
He has another video where he's digging near some lava to the tune of Journey and pretty much the same thing happens, complete with accent and scream. I suspect it may be a running gag.