Zcash was built on the original Bitcoin code base, with many important improvements focusing on privacy-preserving shielded addresses and a community development fund. As such, Zcash transactions are completely private.
The transaction data is posted to a public blockchain, similar to other cryptocurrencies, but with a difference - these transactions can then be verified without revealing the sender, receiver, or transaction amount.
The Zcash coin is ZEC. It can be traded on exchanges, but it can also be mined. ZEC mining is very similar to Bitcoin, and ZEC are created each time a block is added to the Zcash blockchain. Zcash mining is much faster than Bitcoin - they can be mined 8 times more frequently than Bitcoin.