What is the Root Locus?ΒΆ
Simply stated, the root locus is the path traced by the solutions of the closed-loop characteristic equation (often the closed-loop poles) over the s-plane (z-plane for digital systems) as some parameter K (most usually the system gain) is swept over its range, most often from 0 to infinity. As such it gives us a complete picture of all possible solutions to the closed-loop characteristic equation allowing us to pick one that has certain desirable properties. It also allows us to add additional poles and zeros (compensation to the system in an attempt to achieve a desired outcome should the system not achieve it by adjustment of the parameter K alone.
For more formal answer try this question in your favourite search engine: What is the root locus? Please feel free to summarize the answer in the wiki.