A soft fork is a temporary split of a blockchain brought about by a change in the consensus protocol that make previously valid transactions now invalid. Nodes that have not upgraded will still accept new blocks (because they contain only transactions previously considered valid), making the change backward compatible. Only miners need to implement soft forks, and the version with the most hashing power will over time generate the longest chain.
It is different from a hard fork, which is not backward compatible and involves decisions from all users of the blockchain.
Bitcoin went through a soft fork to implement BIP 16 in early 2012 and introduced support for multi-signature transactions.