Voltage, or electrical pressure, in a system produces a proportionate amount of current when placed across electrical resistance. Ohm's law indicates that 1 volt passed through 1 ohm of resistance produces 1 ampere of current, or electrical flow. Voltage and current, therefore, have a direct relationship most of the time.
The lower the electrical resistance of an object, the more easily current can pass through it. The simplest equation is I = V/R, where V is voltage, R is resistance, and I is current. Even relatively low voltages can produce current sufficient to power appliances. Also, there is no such thing as infinite resistance, so even so-called insulators are capable of conducting electricity when exposed to a high enough voltage; lightning is an example of this.
Alternating current muddies the relationship between voltage and current. In an AC circuit, the current constantly alternates direction, hence the name. Typically, an AC circuit includes capacitors and/or inductors, which each bring voltage and current slightly out of sync in their rising and falling phases. In a circuit with an inductor, the voltage leads the current; in a circuit with a capacitor, the current leads the voltage. This keeps a steady flow of power through an electrical appliance.