A Trading Desk is a centralized, service-based organization that serves as a managed service layer, typically between a demand-side platform (DSP) or other audience buying technologies, and an agency.
The Trading Desk uses data from an audience (first party or third party), from the ad exchanges and from the ad server. With all the data collected and related, advertisers can scale their performance.
Big Agencies have Trading Desks in house developed for Advertisers. There are also Advertisers specialized on tech and internet that decided to develop their own Trading Desks, and finally there are independent Trading Desks like Accordant Media and The Trade Desk.