Most of this guide will focus around mining Ethereum, however the way coins are mined can be applied to all crypto currencies.
Ethereum itself is a platform for decentralized applications.
This means that instead of talking to one central server, clients talk to each other. Developers can then build applications that rely on this network to perform tasks distributed among clients in real time. This creates a peer-to-peer network of nodes that perform tasks with one another, similar to how peer-to-peer file sharing protocol BitTorrent works. It’s not the same, but similar enough to compare (“peer to peer” with the “reward” being a file).
The process which you, a miner, is interested in surrounds finding information in a particular block. As the information is found (“mined”) and verified, the worker (you) will receive a reward (Ether) for completing task.
Although this is a broad overview of how mining works with regards to Ethereum, the underlying functionality remains the same. Ethereum is a platform which relies on blockchain technology that is solidified and secured through mined Ether.