Holonomic constraint is a constraint that is derived from the movement of some mechanical device/machine. For instance: a car car go left, right, but cannot turn sharply 90 degrees. If the car turns 90 degrees, it is following an arc (circle). This is what we call holonomic constraint. In case of your problem description, you are writing about pathfinding algorithms used in gaming. Here in case of non-holonomic movement you may imagine a car who can does not have to obey law of physics. A car which could go anywhere you want, turn to any side you want, with any degrees you want. You simply forget that a car has wheels which are limiting the range of your manouvers.
I hope it helped!