There a several ways to mine. At the beginning it was just mining with the CPU, then somebody figured out that a graphic card is more useful and faster to do these monotone calculations.
Then they developed ASICs to do it even more faster.
However, the difficulty increases and so better machines are necessary and all these new machines have something in common: They need more electricity. Somebody already joked and said, we are buying the cryptocurrencies from the power companies.
There are also different algorithm and schemes like PoW (Proof of Work), PoS (Proof of Stake) and now also PoC (Proof of Capacity).
Exactly the last one I will explain more in detail:
A paper wallet is the simplest form of a cold storage. Cold storage can also be in form of a thumb drive, CD, …
The purpose of a cold storage is to have the private key, which is necessary to spend money from the wallet not on a computer. A computer could be hacked, or as we learned from the news, a hard drive could be damaged. The backup is then also a paper wallet.