A flat organization has few layers between the top dawg (CEO) and the bottom line worker.
A flat organization can foster high performance and quick decision-making, because there isn't all the bureaucracy inherent in a multi-layered organization. The front-line worker is much more empowered to exercise judgment and make decisions than in a multi-layered organization. Innovative and entrepreneurial firms typically prefer a flat organization.
A flat organization can be high risk where predictable processes and consistent outcomes are important, because it typically lacks a "best practices" culture.