A flat (or horizontal) organization is an organization that has few or no levels of middle management.
It is different from the hierarchical structure historically adopted by large organizations where people at the bottom of the pyramid must often ask for permission or validation from people higher up before they can take action.
A flat or horizontal organization structure does not necessarily mean that there are no managers left in the organization. There is still a place for managers in flat organizations. However, their role changes.
The role of the manager in a flat organization
In a flat organization, the manager has more time to focus on what matters, i.e. coaching and providing feedback to their teams.