What is Process Management?

Legal Definition
Process management is the ensemble of activities of planning and monitoring the performance of a business process. The term usually refers to the management of business processes and manufacturing processes. Business process management (BPM) and business process reengineering are interrelated, but not identical.

Process management is the application of knowledge, skills, tools, techniques and systems to define, visualize, measure, control, report and improve processes with the goal to meet customer requirements profitably. It can be differentiated from program management in that program management is concerned with managing a group of inter-dependent projects. From another viewpoint, process management includes program management. In project management, process management is the use of a repeatable process to improve the outcome of the project.

ISO 9000 promotes the process approach to managing an organization.

...promotes the adoption of a process approach when developing, implementing and improving the effectiveness of a quality management system, to enhance customer satisfaction by meeting customer requirements.
-- Wikipedia
Legal Definition
Activities related to administration that are aimed at (1) process definition, (2) establishment of responsibilites, (3) evaluation of process performance and (4)Identification of improvement opportunities.