Managing a project consists of executing defined activities to achieve project objectives. These project activities or processes are more or less similar for almost all projects. But depending on the project, stress on each process will be determined by the Project Manager and the project team.
Let us see the general definition of a process before getting into process group.
* A process is a set of interrelated actions & activities performed to achieve a pre-specified product, result, or service.
* Each process is characterized by its inputs, the tools & techniques that can be applied, and the resulting outputs. 
Inputs are the prerequisites or entry criteria to start a process. Output are the exit criteria or the result of the process with which the process ends. Tools & techniques are methods applied on the entry criteria to achieve required results. The output of one process generally becomes an input to another process
or is a deliverable of the project. Defining boundaries of each process ensures better control over the entire project and project objectives.
Project management processes are grouped into 5 different categories called as Process Groups. They are : Initiating, Planning, Executing, Monitoring & controlling and Closing. These process groups provide guidance in applying appropriate project management knowledge and skills during the project.
• Initiating Process Group – Those processes performed to define a new project or a new phase of an existing project by obtaining authorization to start the project. Here is the Input, Tools & Techniques, Output(ITTO) in the form of Mind Map for Initiating Process Group Processes.
• Planning Process Group – Those processes required to establish the scope of the project, refine the objectives, and define the course of action required to attain the objectives that the project was undertaken to achieve.
• Executing Process Group – Those processes performed to complete the work defined in the project management plan to satisfy the project specifications.
• Monitoring and Controlling Process Group – Those processes required to track, review, and regulate the progress and performance of the project; identify any areas in which changes to the plan are required; and initiate the corresponding changes.
• Closing Process Group – Those processes performed to finalize all activities across all Project Management Process Groups to formally close the project.
I added a mind map of project management process groups and processes as per PMBOK 4th Edition in another post – here
Each one of these process groups have well-defined interactions between them. Also, these process groups closely resembles Deming’s PDCA (Plan-Do-Check-Act).
In case of big projects, each of these process group processes can be repeated for each phase instead of defining process groups for the whole project. This extra effort gives more control over the project.
Note on Deming Cycle
Edwards Deming proposed excellent model to analyze business processes in 1950’s. His feedback loop model can be utilized for any cyclic process that takes input from output of previous cycle.
* PLAN: coming up with new or changed process components to improve results. Directly relates to planning process group in Project Management. Either new plans are created during start of the project or plans modified & re-baselined based on inputs from other project processes.
* DO: Implementing the plan and measure its performance. Directly relates to execution process group.
* CHECK: Assessing the measurements and report the results to decision makers. Directly relates to monitoring and controlling process groups.
* ACT: Deciding on changes needed to improve the process. This is the change requests and process changes outputs of monitoring & controlling processes. Project manager & management team review all the change requests/required plan & process changes and approves them.
. PMBOK® Guide – 3rd edition