How do we define drift speed?

In physics, drift velocity is the average velocity attained by charged particles, such as electrons, in a material due to an electric field. The current flowing in a conductor is directly proportional to the drift velocity of electrons. 

The electrons inside a conductor move with random velocities in random directions unless an electric field is applied to the conductor. In general, an electron in a conductor will propagate randomly at the Fermi velocity, resulting in an average velocity of zero.