What is a matrix structure in an organization? Please explain.

Ok, a Matrix
structure is one of the ways that an organization sets up its control and delegation of tasks. 
Lets start by comparing the matrix structure to something that it is not.  Think of a typical
organization with workers, a supervisor, a regional manager, and corporate office management. 
This is a hierarchical structure. 

Think of a matrix structure as the
anti-hierarchy.  Each set of employees is broken up into projects or teams.  The team does not
have a specific "boss," but may have a lead member that helps coordinate activities. 
Each individual employee may belong to several teams, working on many projects at once.  They
might be a leader in one team and a member of another.  By splitting up tasks without delegating
from a central authority (such as a manager), some advocates of matrix organizations claim that
employee creativity and freedom are maximized.  A good example of a matrix organization might be
a software company that is developing several new products.  Each product or project might have
5 members (or more).  These teams are responsible for getting their products into production
without a higher overseeing authority.