tl; dr version: The voltage step propagates as a wave along the wire.
The speed of the voltage-step wave propagation is some fraction of the speed of light, C. For a low-loss coax cable, the speed will be about 0.8 C. For a PCB trace it's more like 0.6 C.
Here's a video with a visualization of wave propagation on a wire, unterminated and terminated: https://www.youtube.com/watch?v=ozeYaikI11g
In this video, the wire (or, more correctly, transmission line) is modeled as a distributed inductance and capacitance. With an unterminated transmission line, the wave bounces back toward the source with the same polarity (adds to the waveform as a positive step.) If it's terminated at the far end, the wave is absorbed at the end. If the line is shorted, the reflected wave is opposite polarity.