There's a rhythm to how a pitcher holds runners, and it matches up against the runner's beat. A pitcher wants to control that rhythm, to enforce his own rules and keep the runner off his. It's easier said than done, for a number of reasons.
Leading off first, a runner can be taking any number of actions when the ball's pitched: getting a good secondary lead and reading the play; or breaking for second on a straight steal; or going hit and run, taking off but peeking in to see where the ball is hit. If the batter's bunting, the runner's making his break the instant he sees the ball dropped down—then his good secondary lead turns full bore, torching it for secondbase.
The pitcher doesn't know what the baserunner's being told, signalled, or deciding on his own to do. But he does know one thing: he knows that he holds the ball and controls the rhythm. He knows what he's going to do before he does it (throw home, throw over, step off, or just hold the set) and that's the key taught to young pitchers: don't get caught mentally betwixt and between. Make your decision and don't tip it off. Handling that decision, disguising it physically and timing it well, all lend advantage to the pitcher. But it's a lot to juggle, and you often see young pitchers—and sometimes veterans—mishandling it, giving light to their own confusion and handing advantage back to the runner (and manifestly to the hitter—the biggest beneficiary of an uncertain pitcher).
Runners, of course, try to break a pitcher's rhythm by juking, faking, taking big leads and splitting his attention. But almost always, the batter's a bigger threat than the runner. The batter advances that runner, cashes him in or leaves him stranded—or grounds a low strike and doubles him up. Dealing with the batter is paramount, but pitchers sometimes literally lose sight of that.
The pitcher's restricted in coming set with a runner on, which balances the advantage a bit back to the runner. First and foremost, the pitcher has to clear the rubber before throwing to a base, unless he's facing that base (like a lefty facing first). Facing the base, he can throw from the rubber but not by pretending to throw home—he has to step toward the base, and can't swing his lead leg or foot back past a certain angle, then throw to the base. Coming set, the pitcher has to bring his hands to a discernible stop, keep his shoulders and legs still, and move only his neck and head to watch the runner. Any other motion below the neck must continue toward home or (within boundaries) toward the base, else it's a balk.
Holding runners is a carefully-practiced part of a good pitcher's repertoire. A righty with a runner on first has it hardest; with that runner directly behind him, he has to come set and use only peripheral vision to watch him—there's no way to face that base without moving the shoulders and twisting the torso. Good pitchers know that peripheral vision is best not for focusing on objects but for discerning motion. Watching that runner peripherally, the pitcher holds his decision point. It teeters in the balance as he remains stock-still from his shoulders down. A good pitcher varies his rhythm there, at the decision point. Seeing motion, he steps off the rubber with his right foot and, if throwing over, he pivots to sling a quick seed, low, right at the closest corner of the bag for a snag-sweep-tag and pickoff. Otherwise, decision snaps his attention from the peripheral runner to the front-and-center batter, and he lets it fly to get that guy out. In his own time, he moves beyond this moment of held breath and puts the game back in motion.