In conducting materials, some electrons are very loosely bound to the atoms of the material. When large amounts of these atoms come together, there is a sort of electron cloud that "hovers" near the atoms of the material. If you examine a cross-section of the piece of conducting material, the electrons will move very quickly through it. This motion is caused by temperature, and electrons flowing in one direction tend to equal the electrons flowing from the other direction, so this is not what causes current to flow. Electrons flow from one atom to another, a process has been compared to the passing of water buckets from one person to another in a bucket brigade.