The word mining bitcoin getwork c section in the context of the gold analogy for crypto currencies. Gold or precious metals are scarce, so are digital tokens, and the only way to increase the total volume is through mining.
Ethereum, like all blockchain technologies, uses an incentive-driven model of security. Consensus is based on choosing the block with the highest total difficulty. Miners produce blocks which the others check for validity. The Ethereum blockchain is in many ways similar to the Bitcoin blockchain, although it does have some differences. As dictated by the protocol, the difficulty dynamically adjusts in such a way that on average one block is produced by the entire network every 15 seconds.
We say that the network produces a blockchain with a 15 second block time. Ethash PoW is memory hard, making it ASIC resistant. Memory hardness is achieved with a proof of work algorithm that requires choosing subsets of a fixed resource dependent on the nonce and block header. As a special case, when you start up your node from scratch, mining will only start once the DAG is built for the current epoch.