Definition of Drift Velocity
If a particle moves in a space in a random manner. That means it continually changes its directions and velocities in a random manner. The resultant of these random motions as a whole called drift velocity.
The definition of drift velocity can be understood by imagining the random motion of free electrons in a conductor. The free electrons in a conductor move with random velocities and in random directions. When an electric field is applied across the conductor the randomly moving electrons are subjected to electrical forces along the direction of the field.
Due to this field, the electrons do not give up their randomness of motion, but they will be shifted towards higher potential with their own random motion. That means the electrons will drift towards higher potential along with their random motions. Thus, every electron will have a net velocity towards the higher potential end of the conductor and this net velocity is referred as the drift velocity of electrons. Hopping, you understand the definition of drift velocity. The current due to this drift movement of electrons inside an electrically stressed conductor, is known as drift current. It is needless to say that every current that flows through a conductor is drift current.
Drift Velocity and Mobility
There are always some free electrons inside any metal at room temperature. More scientifically, at any temperature above the absolute zero, there must be at least some free electrons if the substance is conductive in nature such as metal. These free electrons inside the conductor move randomly and frequently collide with heavier atoms and change their direction of motion every time. When a steady electric field is applied to the conductor, the electrons start moving towards the positive terminal of the applied electrical potential difference. But this movement of electrons does not happen straightway. During travelling towards the positive potential the electrons continuously collide with the atoms and bounced back in a random fashion. During the collision the electrons lose some of their kinetic energy and again due to the presence of electric field, they are re-accelerated towards the positive potential and regain their kinetic energy. Again, during further collision the electrons partly lose their kinetic energy in the same manner. Thus the applied electric field cannot stop the random motion of the electrons inside a conductor. Although in presence of applied electric field, the motion of the electrons is still random, but there will be over all resultant movement of electrons towards positive terminals. In other words, the applied electric field makes the electrons to drift towards positive terminal. That means the electrons get an average drift velocity.
If electric field intensity is increased the electrons are accelerated more rapidly towards positive potential after each collision. Consequently the electrons gain more average drift velocity towards positive potential i.e. in the direction opposite to the applied electric field.
If ν is the drift velocity and E is the applied electric field. 
Where, μe is referred as electron mobility.
Image of Drift Velocity Drift Current and Electron Mobility as shown below:
The current caused by the steady flow of electrons due to drift velocity is called drift current.
AUTHORS
1.Bunty B. Bommera
2.Dakshata U. Kamble