In trying to keep my answer short, Blender Render is the older, legacy render engine that was built for Blender. While it's still available to use, it's no longer being developed.
Cycles is a new and improved render engine with all the new fangled cutting edge tech behind it. And it's very much in development.
So Blender Render is still usable, especially for non-photo-realistic rendering (NPR) and Cycles is your go-to for realistic rendering. But there's not hard and fast rules. Ultimately it's good to know both, the same way it's good for a carpenter to have multiple saws for different kinds of cuts.
