It is said that electric current, which flows in a conductor, conducts electricity. Also in an electric wire free electron flowing in a conductor creates electric current.
As for free electrons inside a conductor, the most common material for a conductor of electric wires is copper and the electron density in 1m^3 is 8.5e28. For example in copper wire, of which length is 1m and the outside diameter is 0.5mm, there are 1.7e22 free electrons, which is enormous. Since copper is one monovalence metal, the number of free electrons and copper ions (atom) are the same.
By the way, free electrons in a copper wire move to random directions with the speed of 1.3e6m/s even in the case of no electric current, which means it is not in electric field. This velocity is called "Fermi velocity" and it exists even under 0 absolute temperature. It is not heat energy and originated from indefinite theory of quantum mechanics. Since electric current is average flow of free electrons, in other word "drift velocity", electric current doesn't exist under this circumstance.
When voltage is put on both sides of a conductor, free electrons increase the speed in proportion to the electric field and by lattice oscillation, lattice defect, and collision with impurities, they will be scattered to different directions from the electric field and lose the speed to the direction of the electric field. Therefore it doesn't increase the speed infinitely and it will keep certain average velocity. That means collision functions as a kind of friction.
As for copper, the time interval between collisions is 5.26e-45 seconds and average drift velocity is,
4.62e-3 (m/s) / (v/m).It means that when 1V voltage is put on both ends of 1m long copper wire, the velocity of free electrons to length direction is 4.62 mm/s. It seems amazingly slow but since electric charge of electrons is -1.6e-19c, 12.6A electric current flows in the 0.5mm copper wire with this speed. You see how large the number of free electrons is.
Now let's think. For example, let's say you put 50mV differential voltage, which is almost a standard limit, on 100m of "10Base-T" cable, which is commonly used for LAN wiring. The electric field that is put on a conductor is 3.7e-5 V/m. Average moving velocity of free electrons is only 1.6e-7 m per second, which is 0.0006 m per hour, and it's far slow than tortoise wake.
If electric current carries electricity and electric current is electron flow, moving velocity of electricity is about the same as walking speed of human. That means that human is able to pass electric current that is conducted on "LAN" wiring so easily and we have to think that electricity is slow.
But on the other hand, we know that telephone and LAN wiring send information far faster than airplanes and when we turn on a switch of a lamp, we see it lights up instantly even if it's in the distance. How can this slow electricity do it? What is speed of electricity? Is it true that electric current conducts electricity?