The Ethereum Name Service (ENS) is built on top of the Ethereum blockchain.
To send Ether or to interact with smart contracts a user needs to have an Ethereum address. For example: 0xb8c2c29ee19d8307cb7255e1cd9cbde883a267d5
When you register a domain using ENS you are sending Ether from your address to the ENS smart contracts. These contracts keep track of the fact that your particular address owns a particular domain.
LabelHash is a web based platform for interacting with the ENS smart contracts. Using LabelHash means that you don't have to understand all of the intricacies of how the ENS smart contracts work and how one goes about interacting with them.
That said, smart contracts are interesting and its always good to understand whats going on behind the scenes. Consider taking a look at our ENS Explained posts.