Process improvement is the act of reviewing a specific process to make it better. The degree of formality can be minimal, such as an immediate decision to change a method on the fly. This might include moving a garbage can closer to a work station to eliminate a walking step of the process. Or, process improvement can be a highly structured, long-term, team-based approach, such as Six Sigma.
One thing to keep in mind it that everything is a process. No matter what it is we want to do, there are a series of linked steps to get a result. Some processes are poor, others are not clearly defined, and still others are hard to repeat, but they still require a series of steps. For example, writing this dictionary entry requires a process. Of course, it is less structured than the one used to build the keyboard used to type it, but it is still a process.
And the power of continuous improvement lies in the fact that any process can be improved.