The act of spinning a small weight attached to a string in a horizontal plane is the study of centripetal motion. The centripetal force is the force that keeps the weight moving in a circular motion as opposed to flying off in a linear motion. Procedural errors are errors in procedure. In other words, mistakes that the person performing the lab would perform. If the weight were not attached securely to the string, that would be procedural error. If the spinning stopper were to accidentally hit a wall or object while spinning, that would also be procedural error.
Experimental error is more related to error that is inherent to the various measurements taken during the experiment. It can be thought of as the difference between the actual value of a measurement and the observed value of a measurement. Examples would include weighing the mass of the stopper and measuring the length of the string (which will be the radius of the circle). Your experimental error here would be directly related the accuracy of the balance used to measure the mass and the ruler used to measure the length. The more accurate you can make these measurements, the less experimental error there will be.