Volt:
Think of the volt as a measurement of electrical "pressure," like you'd find in a common garden hose. For a given diameter of hose, turning up the pressure moves more water. (Water is equivalent to power in this analogy.)
Ampere:
Continuing the garden hose analogy, think of the ampere (aka amp) as a measurement of electrical "flow," with a larger-diameter hose—higher amperage—flowing more water (electrical power) at any given pressure (voltage).
Watt:
Named for James Watt, who also defined the term "horsepower," the watt is a measure of the expenditure of energy over time. The particulars don't really matter here; what does matter is that the watt measures the exact same thing horsepower does. It's just a different unit. Like liters and gallons. One horsepower is equal to 745.7 watts.