Voltage is the difference of electrical potential between two points or two objects. Without this difference of electrical potential, electricity could not be used as a power source.
The number associated with voltage doesn't matter as much as the difference of voltage between two objects or points; this is because zero can be set at any arbitrary point. For example, 60 and -60 volts are the same amount, just oriented in opposite directions. The most common analogy used to describe voltage is that of water pressure building up in a garden hose. High voltage means high pressure, and current occurs when the potential energy is allowed to flow between the two points, similar to water coming from the hose.