A trojan is usually deliberately designed by its author to appear authentic and attractive. For example, it may appear to be a screensaver, a service pack, an application update and so on. Once installed or opened, the trojan may perform its promised function, or display a decoy document to distract the user. In the background however, it also silently performs unauthorized actions (its payload), without the user's knowledge or consent.
Programs identified as Trojan.BitCoinMiners can either function as a miner, or install a separate component that can do so. Malware that use miners as part of their payload are essentially hijacking a user's resources to create cryptocurrency units for the malware author's benefit.
About cryptocurrency mining programs
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.
Cryptocurrency units can be created by any user with specialized mining programs or miners that run the necessary mathematical calculations. Examples of mining programs include Coinhive, Cryptoloot, Electrum, Hashflare and MinerGate, though there are dozens of other similar programs available online.
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.