A set of coins with a focus on private and anonymous transactions. This can be done at various levels.
Some privacy coins make everything obscure, the sending addresses, the receiving addresses, the amount of coins in a transactions - or even wallet - etc.
Monero (XMR) and Zcash (ZEC) are some popular privacy-coins.
Some other privacy coins have optional privacy, where a privacy focused entity can be stay private, but not everyone has to participate.
There are some benefits to each level of privacy, but it's generally a better idea to stay as private as possible.
Many coins without protocol level privacy allow for optional privacy via transaction level protocols. The most common ways are centralized mixing services (which are being cracked down on) and decentralized coin-join and coin-obfuscation protocols such as
cashFusion. These optional privacy protocols often involve multiple transactions, so are best done on low-fee coins. Bitcoin Cash (BCH) with CashFusion is a good example of this sort of privacy.
* All terms and definitions may update as the Cryptionary improves.