The consensus is achieved when all participants of the network agree on the validity of the transactions, ensuring that the ledgers are exact copies of each other.
There are several different mechanisms by which consensus can be reached on a blockchain. The most common, and the one used by Bitcoin is called Proof of Work, and it relies on mining computers to solve a problem before a new block can be created, and transactions can be confirmed.
Consensus when discussing cryptocurrencies can also refer to the rules used by the network to arrive at a consensus and approve transactions. The concept of consensus is key to a decentralized network such as are used in cryptocurrencies.