A distributed contract is a method to form agreements with people via the block chain.
Contracts don't make anything possible that was previously impossible, but rather, they allow you to solve common problems in a way that minimizes trust, allowing human judgements to be taken out of the loop.
Bitcoin can be used to make these arrangements. However there is a number of technology platforms built since 2014 which are designed to for contracts specifically.
Smart Contracts - term coined by Nick Szabo in the late 90's.
Currently, systems allowing to merge a "smart contract" with a human readable text contract has been developed. An example would be a a mutual non-disclosure agreement 
which is written both in text and code.