In short, project management (abbr.: pm) means the application of certain methods for planning, managing and executing a project by the project manager and project staff (or all project stakeholders). The primary task of project management is to achieve all project objectives and milestones taking into account project parameters. The project parameters are usually scope, time and budget - also known as project triangle .
Many terms and techniques are established and standardized, meaning, managing projects entails knowing and applying project management methods that were initially formalized in the early 20th century. One of the pioneers was Henry Gantt who developed what would be named a Gantt-chart (or Gantt-diagram). We nowadays distinguish between traditional project management methods that are based on scheduling project phases in a project network diagram, agile project management that includes methods such as scrum, and hybrid project management which incorporates traditional and agile methods.
Read a more in depth description of project management and agile project management.