The original bilateral contract between two traders is extinguished and replaced by two contracts, each with the clearing-house. This is the precise mechanism that makes futures fungible: your long can be closed against anyone's short because both face the same counterparty.
It also makes anonymity possible. Nobody needs to assess the creditworthiness of the trader on the other side, because after novation that trader is no longer on the other side.
Example: a hedge fund buys 100 ES from a market maker. A second later the fund is long 100 against CME Clearing, the market maker is short 100 against CME Clearing, and neither has any claim on the other.
Related: clearing-house, futures-contract, forward-contract, clearing-member, open-interest