Drift velocity is the average velocity of charged particles (e.g. electrons) in a conductor, caused by an external electric field.
The formula associated with this concept is: $$I=ne\nu A$$
Where $I$ is current, $n$ is charge density, $e$ is the elementary charge, $\nu$ is drift velocity and $A$ is the cross-sectional area of the conductor.
Notice that the greater the cross-sectional area of the conductor is, the greater the current allowed to flow.