A genesis block is the first block of the blockchain. It's assigned to block number 0. It's the only block in the blockchain that doesn't reference to a previous block because there isn't any. It doesn't hold any transactions because there isn't any ether produced yet.
Two nodes in a network will only pair with each other if they both have the same genesis block, that is, blocks synchronization will only happen if both peers have the same genesis block, otherwise they both will reject each other. A different genesis block of high difficulty cannot replace a lower difficult one. Every node generates its own genesis block. For various networks, the genesis block is hardcoded into the client.