The battery supplies a part of its chemical energy to the electrons that emerge out of it. These energized electrons lose this energy in the outer circuit, when they go through various electronic components. The electrons in a simple conductor collide due to their thermal energy.
Electrons move from the -ve terminal of the battery to the +ve terminal. In a reverse-biased diode, the electrons move from minority region (the p side) to the majority region (the n side) due to the electric field inside the diode which forces the charges from their minority region into their majority region.
Current is defined as the number of charges passing unit area of conductor per sec. The electrons inside a conductor without a battery, suffer a lot of collisions but their velocity on an average can be considered $0$ and hence, they are unable to produce current.
But when a battery is joined across the conductor an electric field is set up in it. Even in the presence of this electric field, the free electrons suffer a lot of collisions but now their movement gets a certain direction. The real motion is still zig-zag but with a certain direction. The high number of collisions are responsible for their slow drift speed.
As the electric field starts to accelerate the electron, the electron collides and loses its kinetic energy in form of heat. Then the field accelerates the electron again but the electron again collides and this goes on.
The electrons drift through the conductor and their speed ,in presence of E.field, is called drift speed. Although the drift speed of electrons is very low $( −0.000023 m/s)$ a large current is produced because of their high quantity crossing per unit area of the conductor per sec, which is about $10^{23}$ electrons.
Best Answer
When electricity was discovered, scientists at that time were not aware of electrons. They thought that positive ions were responsible for current. Therefore, they decided that the direction of current would be from positive to negative. We still respect this convention even today.
After a century, J. J. Thomson discovered electrons. It was soon understood that electrons were responsible for current in most conductors. Changing the convention seemed to be a bad idea. Hence, we continued to use the same convention.
TL;DR: By convention, current is assumed to travel from positive to negative direction. The electrons travel from negative to positive. The direction of current is not the same as direction of flow of electrons; they are opposite.