Referred to as drift velocity, a single electron will mosey along at a mere 23 micrometers per second through a 2 mm diameter copper wire.
Electrical signals travel from a point A to a point B at lickety-split velocity. Electrical signals travel through a coaxial cable from source to load at roughly two-thirds of the speed of light, for example. However, the movement of particles of charge through an electrical conductor is nowhere near that fast. Referred to as "drift velocity," a single electron will mosey along at a mere 23 micrometers per second (51.75 micro-miles per hour) through a 2 mm diameter copper wire. There is a very nice description of this to be read on Wikipedia.
There is a mechanical analogy which we can examine as follows, to wit, a yardstick being pushed at one end by the tip of a finger which causes a mass at the other end of the yardstick to move.
Whatever energy it takes to move the mass through some distance is supplied by the finger tip at the left end of the yardstick. The finger nudges a first granule of wood which nudges the next granule of wood which nudges the next ... until the final granule nudges the mass. The energy transfer from fingertip to mass happens so quickly that you can't actually see it. That energy goes lickety-split down the yardstick's three-foot length but the yardstick itself just barely moves at its drift velocity.
In the copper wire, electrical excitation nudges a first electron which nudges the next electron which nudges the next ... until the final electron excites the load. This analogy isn't perfect, but it does illustrate the conceptual difference between a signal's propagation velocity versus a charged particles' drift velocity.
John Dunn is an electronics consultant, and a graduate of The Polytechnic Institute of Brooklyn (BSEE) and of New York University (MSEE).