Take a 10 ft plastic pipe of the same diameter as ping-pong balls.
Fill this pipe from start to end sequentially and fully with ping-pong balls.
Now stick your finger in one end.
While you only moved the ping-pong balls a few inches, almost immediately a ping-pong ball will come out the other end... The "signal" "traveled" at a much faster speed than the actual ping-pongs.
To visualize electrical signals, imagine a tube completely full of balls. When you push a new ball into one end, a different ball comes out the other. The effect of adding the ball is seen very quickly (i.e. a change in the field), but the speed the ball moves through the tube (i.e. how fast electrons move through the conductor) is quite different.