Bisq is a cross-platform desktop application that allows users to trade national currency (dollars, euros, etc) for bitcoin without relying on centralized exchanges such as Coinbase, Bitstamp or (the former) Mt. Gox.
By running Bisq on their local machines, users form a peer-to-peer network. Offers to buy and sell bitcoin are broadcast to that network, and through the process of offering and accepting these trades via the Bisq UI, a market is established.
There are no central points of control or failure in the Bisq network. There are no trusted third parties. When two parties agree to trade national currency for bitcoin, the bitcoin to be bought or sold is held in escrow using multisignature transaction capabilities native to the bitcoin protocol.
Because the national currency portion of any trade must be transferred via traditional means such as a wire transfer, Bisq incorporates first-class support for human arbitration to resolve any errors or disputes.
You can read about all of this and more in the whitepaper and arbitration documents. Several videos are available as well.