It is an obvious that everyone has seen wheel or cylindrical objects moving forward due to the rotational force (torque is the right term for this one). However, if you ask yourself a question, how does such torque leads to the forward motion rather than only rotation, you will get puzzled. I was also very much confused to answer this question. I spent lot of time and energy to find the answer for this question. However, the answer is provided by some fundamental laws of physics, which we studied during our high school. In the next few sections, I will try to elaborate the answer by simple explanations and figures, as I can provide.
Lets start with a wheel, which is rolling and moving forward , as given in Fig .1.
Figure 1: Wheel with applied torque
In the figure torque is applied in clockwise direction. This torque can be replaced by a couple passing through the boundaries of the wheel (Fig .2). Couple consist of equal and opposite forces that causes only rotation. Now the force (F1) that is acting in the bottom of the wheel is opposed and cancelled by static friction Fr. (Static friction is also known as dry friction. It exists between two sliding bodies and resists the sliding of one object over another). The direction of Fr is opposite to the applied force. Since the F1 is cancelled by Fr, remaining force F2 makes the wheel move forward. 
Figure 2: Torque is replaced by a couple
So the main cause of rolling for any wheel is the static friction. The static friction is never greater than coefficient of friction times Normal force to the wheel. When the applied force due to the torque is greater than this value, then wheel starts slipping. This is the reason why a vehicle does not move forward when its wheel is stucked in mud.
