Amperes (or Amps) are the standard measure of electrical current. Much like water flowing through a pipe, Amps measure how much electricity is moving through a wire at any given time. The Amp draw of a circuit is dependent on the needs of the devices plugged into it, but is always limited by a branch circuit breaker.
Volts are the standard measure of electrical potential and are a fixed value for every circuit. Volts are measured with respect to a reference point (usually between the two respective legs of the circuit). As one increases the electrical potential between two points, the amount of potential energy available increases. For example, consider a rock dropped from 3 meters versus one dropped from 30 meters. The rock dropped from 30 meters will be going much faster when it hits the ground than one dropped from 3 meters and exert more energy on the ground as it hits. Until the rocks are dropped, that energy exists only as potential. Similarly, a 208V circuit has about 1.73 times the potential energy of a 120V circuit, when drawing the same amount of current.
Watts are a measure of the total power being consumed by a system. The simplest calculation is: Watts = Volts x Amps. This is the measurement that power companies use for billing and is also known as Volt-Amps. A true RMS calculation of Watts takes into account the shape and phases of the voltage and current wave forms being delivered to a circuit to provide a reading of the power being used by a circuit. Any difference between the RMS value of Watts and the Volt-Amps value indicates inefficiencies in the way power is being used by the equipment on the circuit.