A "self organizing team" has the authority to choose the work that it will perform and the responsibility to do that work in the way that it chooses.  Important aspects of a self organizing team are:

1. The team selects its own work. At the beginning of an iteration the team collectively selects the work items from the prioritized Work Items List. Work selection is performed within given constraints, including the priorities set by Stakeholders, time (such as the length of the current Iteration), the budget, and the skills of team members.
2. Individuals select their own work. Individuals are empowered to select their own work. Someone will choose to do something because they are good at it and know that they can do the work effectively, because they want to gain more experience at something and hope to improve their skill-set by working with someone with such experience, or because they know that the work needs to be done and that it's their turn to do so. Although an individual fulfills one or more roles on a project team that doesn't imply that the person is constrained to only doing specific types of work.
3. The team determines how to perform the work. At the beginning of an iteration the team will hold an "all hands" planning meeting where it determines the general strategy for doing the work and the tasks required to do so. More detailed planning, if required, will be done on a just-in-time (JIT) basis by the individual(s) doing the work. Note that the team is still constrained by your organization's standards, technical infrastructure, regulations, and so on.
4. Everyone commits to the work. The team commits to accomplishing the work that it has agreed to do by the end of the iteration. Individuals also commit to doing the work that they say they will do, although as the iteration progresses various tasks may be renegotiated as required.
5. The team coordinates regularly. To ensure that the work is accomplished the team must coordinate its efforts effectively. This is typically done through daily stand up meetings of the team and impromptu discussions between individuals.

This is a participatory approach to decision making where everyone has the opportunity to provide input and to listen to the decision making process. The goal is to make decisions at the right place within the organizational structure, empowering teams by giving them both the responsibility and the authority to get the job done. It improves motivation amongst team members, and thereby their productivity, by giving them control over their work.

Project Manager Responsibilities

There is still work for the Project Manager on self organizing teams. The project manager must still:

1. Provide leadership. Team culture and project vision must be nurtured and evolved throughout the project, and direction must be provided to the team.
2. Mediate disagreements. The manager must be prepared to step in and make a decision when other team members are unable to come to a decision.
3. Ensure that team members grow their skill-set. From time to time the manager may need to motivate individuals to take on new tasks that are outside their comfort zone or to work with others to help those people gain new skills.
4. Ensure that the team respects their limits. Self organizing teams have the authority to make decisions within the scope of their responsibility, but that doesn't mean that they get to rethink everything that they feel like. For example, the development team must still conform to the technical infrastructure and to the business strategy of your organization: they likely don't have the authority to change these things even though they may not fully agree with them. When an issue falls outside their scope of responsibility the team must either accept it or collaborate with the people with the appropriate authority.
5. Summarize the project plan. External stakeholders, such as senior management or business representatives not actively involved with the team, will want to know the current status of the project and the team's current plans. The project manager may be required to summarize and communicate this information to those people.

What This Isn't

The concept of self organizing teams often sounds like anarchy or non-management to traditional IT professionals, but nothing could be further from the truth. Although self organization relies on team members being responsible and mature it is tempered by the guiding hand of a good project manager. It is also tempered by organizational standards, infrastructure, and external regulations. "Self organizing" doesn't mean that you have complete freedom to do what you want.

Self organization isn't necessarily a consensus-based approach either; sometimes individuals will disagree with a decision but will choose to go along with the will of the team. Nevertheless, consensus isn't ruled out by this approach but it certainly isn't required.