ZeroCoin is a privacy protocol that was originally designed as an extension to Bitcoin. Its overarching purpose was to improve the assets on-chain anonymity by having a process known as coin-mixing happen automatically.
The Zerocash protocol was decommissioned not long after 2014 and replaced with the new Zerocash protocol. This new and improved Zerocoin 2.0 allows direct anonymous payments between parties. A Zerocoin transaction can exist alongside the Bitcoin currency ( which is non-anonymous). Users of the protocol can convert (non-anonymous) bitcoins into (anonymous) coins, called zerocoins. Users then send zerocoins to other users and split/merge the used zerocoins in any way that preserves their total value. As used can covert into the zerocoins, they of course can also convert zerocoins back into regular bitcoins, although in principle this is not necessary: all transactions can be made in terms of zerocoins.