Question

What is an electric current? How does it flow in a wire? How fast do the electrons move?

Answer 1

In simple words

Electric Current is nothing but flow of free electric charge ,most oftten electrons.

In wire which is made up of metal we have free electrons on surface of wire which flow in a direction of Voltage difference (Charge Difference).

Last Part of question is little bit tricky as there are three kinds of speeds associated with electron movements in a wire.Namely signal speed, the Fermi speed, and the drift speed.

But to answer in general to get a rough idea ,for the case of a 12 gauge copper wire carrying 10 amperes of current (typical of home wiring), the individual electrons only move about 0.02 cm per sec or 1.2 inches per minute (in science this is called the drift velocity of the electrons.)