Ohm's Law states that electric current is directly proportional to potential difference, and inversely proportional to the resistance of the conductor. This is expressed by the equation I = V/R, where I is the current, V is the potential difference and R is the resistance of the circuit. R is a constant and does not depend upon the current (this is assuming constant temperature).
The best depictions is by a reference to the flow of water through a pipe. The flow of water increases with increasing pressure difference between the two ends, and decreases with any narrowing of the pipe. In this analogy the volume of water flow represents current, water pressure represents potential difference and the diameter of the pipe represents resistance.
Ohm's Law is empirically based, meaning it is derived from experiment and observation, rather than being formulated from abstract theory. While some materials may deviate from Ohm's Law under certain conditions, it is generally obeyed on various scales and circumstances. It has proven reliable in silicon conductors with dimensions as small as four atoms by one atom.