A force is a critical influence on motion. Some forces visibly change the speed or direction of motion. Other forces convert macroscopic motion to microscopic motion. A non-conservative force is the classification given to any force whose work is dependent on the path taken because microscopic effects are dependent on macroscopic phenomena. In short, a non-conservative force converts macroscopic motion into microscopic motion.
An example of non-conservative forces in a baseball game:
All real systems have some non-conservative forces associated with them. For example, when the moon rotates around the Earth it creates tidal forces, which will slightly warm the oceans (microscopic motion of the molecules in the ocean). However, it is a small effect compared to the energy in the system.
By the second law of thermodynamics, all systems lose mechanical energy over time. It is important to note that non-conservative forces do not destroy energy they just convert it into a less useful (less ordered) form.
The University of Colorado has graciously allowed us to use the following PhET simulation. It explores how friction turns macroscopic motion into microscopic.
To learn more about conservative and non-conservative forces, please see hyperphysics.