1. One, it is an accounting process to verify, validate, and record cryptocurrency transactions on an online, public, and encrypted ledger - called the blockchain. This is done by installing a CPU/specialized computers, called miners, along with the verification software of the cryptocurrency.
2. Two, it is also the process for minting new coins and bringing them into public circulation. This is also done to incentivize or reward those who install their computers for the purpose laid out in point 1. Mining is usually a voluntary activity. Hence incentivization plays a big role in it.
In short - a cross between an accountant and a gold miner.
There are multiple types of mining CPUs depending on the type of coin or token being mined and the consensus mechanism being used e.g. Proof of Work or Proof of stake etc.
There are roughly 500 mineable coins or tokens today.
All you need is the infrastructure to do it. Some of which are expensive to install and maintain. e.g. ASIC miners used for Bitcoin mining. They are heavy duty computers which have been manufactured specially to mine bitcoin or bitcoin forked coins like bitcoin cash.
However, it should be noted that solo mining or an individual mining bitcoin is usually not very profitable. It is wise to get into bitcoin mining through pools or through those who have cloud mining infrastructures. There is also a related environment requirement.
There are many companies who are especially setting up mining plants.