When you dilute developer, you change the chemical characteristics of the various components. The two effects most cited are that you get better sharpness, but at the same time slightly larger grain - both caused by the suppression of silver solvent action. You also can gain a bit more speed, and because of the extended developing times, it is easier to get even and consistent development. Dilute developer makes it economical to use it one-shot (throw it away after usage), which further adds to consistency.
In howfar the effects of dilute developer are visible, depends on the film/developer combination. When starting out with a new combo, test various dilutions and see whether you can make out any differences. Use what you like best.