If your handlebars were connected directly to your steerer tube, then the bars would pivot on the axis of the steerer tube as it turned back and forth. Most upright bikes have stems of 80-130cm offset, ahead of the stem. As the steering is turned, the handlebar describes a small arc, ahead of the steerer tube. The effect is small and it doesn't bother most DF riders. I call that 'reverse tiller.' Many recumbents have a stem that puts the handlebars behind the axis of the steerer tube. If the offset is small, then it's not noticed. But if the offset is large, then steering the bike from one side to the other causes the handlebars to describe a large arc instead of a simple pivot motion. At the far extremes of steering, the entire bars can end up way off to one side of the bike! When the effect becomes noticeable, it's referred to as 'tiller.'

Tiller isn't necessarily bad. For the praying hamster position, when the arms are hanging from the bars, the arms' weight tends to help center the steering, making it stable when riding in a straight line. Where it becomes a hassle is in slow-speed, tight turns, where it requires moving the hands through a larger distance in order to turn the bike.