Nice Wikipedia info (note: I am a retired PM and have had a CAPM certification since 2005):
The Project Management Body of Knowledge is a set of standard terminology and guidelines (a body of knowledge) for project management. The body of knowledge evolves over time and is presented in A Guide to the Project Management Body of Knowledge (the Guide to the PMBOK or the Guide), a book whose fifth edition came out in 2013. The Guide is a document resulting from work overseen by the Project Management Institute (PMI), which offers the CAPM and PMP certifications.
The five process groups are:.
1.Initiating: processes performed to define a new project or a new phase of an existing project by obtaining authorization to start the project or phase.
2.Planning: 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.
3.Executing: Those processes performed to complete the work defined in the project management plan to satisfy the project specifications
4.Monitoring and Controlling: 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.
5.Closing: Those processes performed to finalize all activities across all Process Groups to formally close the project or phase.
The ten knowledge areas, each of which contains some or all of the project management processes, are:
1.Project Integration Management : the processes and activities needed to identify, define, combine, unify, and coordinate the various processes and project management activities within the project management process groups.
2.Project Scope management : the processes required to ensure that the project includes all the work required, and only the work required, to complete the project successfully.
3.Project Time Management : the processes required to manage the timely completion of the project.
4.Project Cost Management : the processes involved in planning, estimating, budgeting, financing, funding, managing, and controlling costs so that the project can be completed within the approved budget.
5.Project Quality Management : the processes and activities of the performing organization that determine quality policies, objectives, and responsibilities so that the project will satisfy the needs for which it was undertaken.
6.Project Human Resource Management : the processes that organize, manage, and lead the project team.
7.Project Communications Management : the processes that are required to ensure timely and appropriate planning, collection, creation, distribution, storage, retrieval, management, control, monitoring, and the ultimate disposition of project information.
8.Project Risk Management : the processes of conducting risk management planning, identification, analysis, response planning, and controlling risk on a project.
9.Project Procurement Management : the processes necessary to purchase or acquire products, services, or results needed from outside the project team. Processes in this area include Procurement Planning, Solicitation Planning, Solicitation, Source Selection, Contract Administration, and Contract Closeout.
10.Project Stakeholder Management : the processes required to identify all people or organizations impacted by the project, analyzing stakeholder expectations and impact on the project, and developing appropriate management strategies for effectively engaging stakeholders in project decisions and execution.
Each of the ten knowledge areas contains the processes that need to be accomplished within its discipline in order to achieve effective project management. Each of these processes also falls into one of the five process groups, creating a matrix structure such that every process can be related to one knowledge area and one process group. The current PMBOK describes 47 process groups.
An example: You have been selected as Project Manager for a team of 4 students to present a 10-minuted presentation for your PM class next week. Your team as a whole will receive a grade and each member will receive an individual grade. You are responsible for selecting a topic, making assignments for developing and presenting the presentation, making/buying of materials, etc., etc. -- (so you don't do everything, but you need to know about "various activities involved in project management." One very important item is risk: what will you when something breaks, someone gets sick or doesn't complete their assignment, your presentation is moved to an earlier date, ... (well, you get the idea).