Project Management is the management of projects, would be the simple answer. The next question to ask is what makes project management different from other forms of management. The most obvious 'other' management to look at would be the day-to-day or line management of an organizations. As we saw in the article what is a project? the key characteristic of a project is the temporary nature and the the fact that projects create change. Most line management is based on steady state. Keeping things the way they are.
Before we delve a bit deeper into what the some of the key elements of project management are, we need to point out that all types of management have one thing in common, and that is the word management. So what is management? The etymological origin of management (the act of managing) from the verb to manage + ment. Manage is based on Latin, Manus - Hand and subsequently Italian, Maneggiare - to handle. The ~ment suffix is added to the verb stem indicating "the result of". Therefor the meaning of management is "the result of handling (something)". The original something was a horse but from the 16th century on also objects/subjects or businesses were included.
In today's context, management is the act of making objects/subjects do things they otherwise would not do by themselves. In one of the next chapters we will discuss in a bit more details some of the common elements of all types of management.
Since projects are the subject of project management it is easy to understand that some of the key elements of project management are dealing with change, focus on a defined (or not) end result. Both the end and result are important here. The end because projects are time-bound and result since projects are focused on creating something new, something unique. Unique does not necessarily mean 'never done before' but more unique in terms of the specific result.
The final, important element is uncertainty. Since projects create change, something new, in a defined context of time, cost and quality they inevitably deal with uncertainty.