Ethfinex is the sister company of Bitfinex,one of the world's largest cryptocurrency exchanges. As we all know, centralized exchanges are a security risk. With decentralized exchanges. it can be difficult to build an order book and they are slow and inefficient. The non-custodial exchanges, like Shapeshift and Changelly, do not have order books.
Ethfinex is looking to bridge the gap with a hybrid exchange that will eventually be owned by the traders themselves.