Voltage is a measurement of forces that make electrons move from point A to point B. The unit of measurement is called volts, and it's ALWAYS measured of one point to another. The resulting voltage is the electric potential of B relative to the electric potential of A. That's why voltage is also called electric potential difference.
Let's say we take a voltmeter or multimeter and we place its two probes on a conductor. We get a reading that says 5v, for example, meaning 5 volts of voltage. If we removed those probes and switched places, so the black probe is where the red probe was, and vice-versa, the reading would say -5v, or negative 5 volts. That's because it's the same absolute electric potential difference, it's just going the opposite way this time.
Another way to think about is that if the electrons are moving forward, the volts are positive, and if they're moving backwards, the volts are negative. Unfortunately, I'm not sure if that's exactly how it is, because I think I've heard that the way it works in electrical engineering is that it's actually positive when they're going backward. I'm not really sure. To be honest, it doesn't really matter. The point is, if it's positive it's one way, and if it's the negative it's the opposite way.
Many appliances do not care if the voltage is negative, as both negative and positive voltage mean the same amount of electrical energy can be consumed. A lightbulb, for example, will emit light no matter which direction the electrons pass through it.
Electronic devices, however, are more complicated. The algorithms physically carved in electronic circuits expect electricity to always go in one direction, so every electronic device has a circuit called a rectifier that converts AC current into Direct Current (DC), which always has positive voltage instead of alternating voltage.
Finally, it's worth noting that positive and negative voltage has absolutely nothing to do with positively charged particles (protons) and negatively charged particles (electrons). The subatomic particles that jump from one atom to another in a conducting material, creating electricity, are only the electrons. The protons just stay in the nuclei. It's called electricity, not protonicity. The only thing that those terms mean is that protons are opposite to electrons in the sense that protons attract electrons, protons repel other protons, and electrons repel other electrons. It's completely irrelevant when we talk about voltage.