A cryptocurrency is an anonymous, decentralized form of digital currency, which can be used online as a medium of exchange much like traditional, physical currencies. Multiple cryptocurrencies exist, such as BitCoin, Ethereum and Monero.
The 'crypto' part of the term refers to the use of cryptography both for creating the currency units and for securing transactions made with the units. Because of the anonymity provided by cryptocurrency, its legality and acceptance varies considerably between countries.
About cryptocurrency mining programs
Cryptocurrency units can be created by any user with specialized mining programs or miners that run the mathematical calculations needed to generate a unit of a particular cryptocurrency. Examples of mining programs include Coinhive, Cryptoloot, Electrum, Hashflare and MinerGate, though there are dozens of other similar programs available online.
Because the calculations are complex, many enthusiasts will build computers with specialized hardware and software to handle the work. Some websites also support cloud mining, where users visiting the site essentially allow temporary use of their computer's processing power to perform part of the calculating work, usually in exchange for a service offered by the site.
Some malware include miners as part of their payload; in such cases, the malware is hijacking a user's computer to create cryptocurrency units for the malware author's benefit.