Many measurements are taken with respect to a reference. That means, for example, you can measure a distance from here to there, so “here” is your reference.
Most voltages are measured with respect to a reference, commonly called “ground” or “earth.” If you connect a power supply with its positive connection to ground, then the negative connection will have a negative voltage compared to ground.
In order for any voltage to cause a current, it must be connected to a circuit, which means that there is a continuous path for the current to flow from the power supply, through the load and back to the power supply. The electrons flow from the negative pole of the power supply, through the circuit doing the work (a “load”) and back to the positive pole of the supply. Many components can only function if the direction of the current is correct (“correct” depends on the device being powered), so polarity is usually pretty important. Incorrect polarity on a DC motor will cause the motor tomspin backwards, for example.
Another analogy is temperature. I’m pretty sure you’re familiar with temperatures below zero - negative temperatures. Complicating things is the fact that Farenheit and Celcius use different references for their zero points. All these measurements simply depend on a reference point, so the measurement is a comparison to that point. Altitudes are usually referenced to sea level, and you can go below sea level (Death Valley, for example) - negative altitude.
