To make any change to the Ethereum blockchain, a transaction must be sent. A transaction is a cryptographically-signed message that specifies what change is to be made, and it is sent to any node in the network. Based on Ethereum’s rules of consensus, the network then agrees that the transaction is a valid one, and it is included in a block that is added to the blockchain.
The simplest type of transaction is a token transfer, which involves transferring ETH from one account to another.
Smart contracts, like the ones used for ENS, also function through the use of Ether transactions. Each time someone interacts with a smart contract, this action also takes place through an Ethereum transaction.
In order to incentivize miners to assume the heavy burden of cryptographically securing the Ethereum blockchain and make changes to it, each transaction incurs a cost called a "gas fee".
More comprehensive information on how transactions work can be found in this article and in the ethereum documentation.