This game uses 8 by 8 by 8 blocks so that you will mine with them.
The blocks are aligned to a grid so that it will look better and more easier.
When you mine a block, more blocks will fill your area so that it won't lag.
If the entire mine just generated at once, it will lag so much that everyone will be disconnected and gameplay would be much harder.
Ores actually generate at random. They use a coordinates system to know where to place rare ores and where to not.
When you mine at a specific coordinates, the game figures out what layer is supposed to generate at the coordinates.
Also, it's impossible to die by falling off world because Network Streaming is disabled.