The quotes and analysis in these articles comes, with permission, from the wonderful Teal wiki.

“Teal Organisation Leaders have a role of “holding the space” of distributed authority.”
Wiki
Whenever people in the organization, consciously or unconsciously, revert to traditional management control mechanisms, the leader reminds everyone about the fundamental assumptions and encourages them to find solutions in line with the self-managing nature of the organization. Leaders demonstrate their wholeness by being transparent, potentially vulnerable. Some revolutions also understand Leadership as primarily having this support function. The Committees for the Defense of the Revolution in Cuba, The Revolutionary Indigenous Clandestine Committee of the Ejército Zapatista de Liberación Nacional.
“In previous organisational systems, the pyramidal structures are built on the (often unconscious) assumption that people cannot be trusted and must be controlled by their hierarchical superior.”
Wiki
There is a natural tendency for people in dedicated staff functions within the pyramids, often with the best of intentions, to prove their worth by finding ways to “add value” by devising rules and procedures, building up expertise, finding new problems to solve. Dis-economies of motivation are produced.
In the peer-to-peer Teal team networks, tasks typically performed by support functions are, whenever possible, done by front-line teams themselves. Employees or teams do the analysis, create the necessary specifications, visit and negotiate with suppliers, and even secure financing from the bank if needed. Where standards are useful, members use the Advice Process to inform decisions and work. Supporting teams and Supporting roles often exist, but HR, sales and marketing do not exist as self-managing teams need direct staff to customer contact. Middle management is replaced by regional coaches, hub leaders to help them work through problems. But final decision making rests with the teams, bounded by the required Advice Processes, and questionable by a binding but non-aggressive form of Conflict Resolution. This is similar sometimes to Sociocracy and Holacracy, structured in concentric [nested] circles, where decisions are not sent upwards, and cannot be overturned by members of overarching circles.
Coordination & Expertise
“Teal organizations allow expertise to develop in a distributed fashion.”
Wiki
Coordination is in effect created when a colleague reaches out to other colleagues with the Advice Process to share her proposed decision and listens to their advice. Over time, colleagues in front-line teams build up a lot of specialized knowledge. A machine operator might know all about the use of a certain lubricant, a home-care nurse all about a certain arcane medical condition, or an engineer all about how to create a complex financial tool to calculate a new machine’s return on investment. Rather than establishing staff roles for these experts, Teal organizations aim to help team members identify colleagues with the right expertise. It can be highly motivating for people to be sought out by colleagues for advice and expertise. Special systems for sharing information are common, such as internal social networks and knowledge platforms. In many cases, Volunteer Task Forces can be set up to codify and disseminate knowledge in specific areas (through central knowledge repositories, training, etc.). Finally, expertise in certain areas (say about labor law in Human Resources) can be contracted from the outside. Rather than hiring an expert into a staff role, a freelancer or consultant can be used as an advisor when needed by members of front-line teams.
Bureaucracy
There are no project or program managers, no HR, no software systems or Gantt charts to organize or control the various projects underway. There is minimal project budgeting, no master plan and rarely a timeline. A huge amount of time is freed by dropping all the formalities of project planning— writing the plan, getting approval, reporting on progress, explaining variations, rescheduling, and re-estimating.
Teal Organisations benefit from an invigorating culture where there are almost no barriers to activity. Reducing bureaucracy is key, having more varied skills in each team helps, using the Advice Process is natural, organic and emotionally enjoyable.
“The centralized planning committees of the Soviet Union were ineffective and the contemporary approaches to capitalism leave much to be desired.”
Wiki