Conservative and non-conservative forces
Conservative force are those forces have the property that the work done in moving a particle between 2 points is independent of the path taken Equivalently, if the particle moves in a closed loop, net work done by a conservative force is zero.
It is possible to describe a numerical value of potential at every point in space for a conservative force. When an object moves from 1 location to other, the force changes the potential energy of object by an amount that does not depend on path taken.
Nonconservative forces arise because of the neglected degrees of freedom. For instance, friction can be treated without resorting to the use of nonconservative forces by considering motion of the individual molecules; but that means every molecule's motion should be considered rather than handling it through statistical methods. For the macroscopic systems nonconservative approximation is simpler to deal with than the millions of degrees of freedom. The examples of nonconservative forces are friction and non-elastic material stress.
The term conservative force comes from the fact that when the conservative force exists, it conserves mechanical energy. The familiar conservative forces are gravity, the electric force and spring force.
A number of forces are not force fields. In these cases, the 3 conditions stated above are not mathematically equivalent. For instance, the magnetic force satisfies 2nd condition (since the work done by a magnetic field on a charged particle is always zero), but does not satisfy 3rd condition, and 1st condition is not even defined. Accordingly, some of the authors classify the magnetic force as conservative, while others do not. It should be emphasized that the magnetic force is an unusual case; the velocity-dependent forces, like friction, do not satisfy any of the 3 conditions, and therefore are unambiguously nonconservative.