EDS = Equity Default Swap
An EDS is a derivative contract between two parties - a protection buyer and a protection seller - whereby the former has the right, in exchange for the regular payment of a fixed premium, to receive from the latter a floating protection amount in case of a "trigger" event.
They are therefore similar to credit default swaps, with the only difference being the definition of a trigger event. In an EDS, a protection payment event is not triggered by a credit event as in a CDS, but when the stock price of the reference entity falls below a certain low threshold.
It is somehow similar to a deep OTM America digital put.
As CDS, they are also quoted as spreads over Libor. Because an EDS is more likely to be triggered than a CDS, they generally trade at higher spreads than CDS.