Ohm's law depends upon the property of conduction of a material. It is obeyed by some materials and disobeyed by some others.Here we explain that why metals obey this law.
In metals the valence electrons are most loosely bound to their to their respective atoms and some of these loosely bound electrons behave as free electrons at room temperature.

The motion of free electrons in metals is similar to motion of molecules in a gas, that is why metals are sometimes called electron's gas. However unlike gases the velocities and hence the energies of free electrons in the metals have a very small range.

Moreover the velocities of free electrons are almost independent of temperature whereas velocities of gas molecules totally depend upon the temperature. In abscence of electric field electrons random direction of motion. The direction of motion is changed when electrons collide with each other.
MEAN FREE PATH:-
The average distance covered by free electron between two successive collisions of free electron with another free electron is called mean free path of the free electron.

MEAN FREE TIME:-
The average time between two successive collisions of free electron with another free electron is called mean free time of the free electron.

When an external electric field is applied then the electron gets a drift velocity, and a drift motion occurs which is opposite in direction to the applied voltage. This drift velocity is much more than the earlier velocity of electrons.