Formulas:
Watts = Amps x Volts {can also be written Power = current x voltage}
Amps = Watts / Volts
Volts = Watts / Amps
Watt-Hours = Volts x Amp-Hours {or energy = voltage x current x time}
Skier Analogy:
Imagine your electrical system as a mountain with chair lifts and some skiers on it.
The voltage of an electrical system is comparable to the height of the chairlifts, i.e. the amount of potential energy per unit (skier or electrons). If you have ten small chair lifts (12V) you can either put them all in a row up the hill which adds the height of each getting your skiers pretty high up the hill (giving 120V) or can have them all next to each other allowing more skiers to go up the mountain but not as high (12V).
Amps are the number of skiers travelling on our little mountain circuit (from the bottom up the chair lift then back down the slope to the bottom). In the example above stacking the chairlifts up the mountain (series connection) gives a lot of height (10x voltage) but limits the amount of skiers (1x amps) that can go up the mountain. Having the chair lifts all next to each other (parallel connection) allows lots of skiers (10x amps) to go through the circuit but they won't go as high (1x voltage).
You can think of power sources (like batteries) as chair lifts i.e. they add energy to the system by taking the skiers up the hill. Power consumers (motors, resistors etc) are like the downward slope of the hill, the energy that was given to the skier by the chairlift is used when they go down the runs on the slope. The cables that join everything is sort of like the skier cutting across the mountain without going down very much. The skier can get to the slope (eg. motor) where he wants to go without losing much of his height (cables have a small resistance but generally don't drop much voltage across them).
Power is like an instantaneous (not influenced by time) measure of how much fun people are having in your resort. You get enjoyment happening when people travel down the runs on your hill. Having a few people (small amps) on very long runs (high volts) is the same amount of overall fun (watts) as having lots of people (high amps) on a small run (low volts). When you have too many people (amps) on the same small run they start to melt the snow away (melt wires, burn out motor etc.) but if your skiers have too much height and speed (volts) they might break the more fragile bits of the circuits as the go past them (i.e. motor brushes).
Water analogy:
Voltage is defined as difference of potential. The Volt is the SI unit of measurement of this potential. Voltage is analogous to water pressure in a pipe. Voltage is the electromotive force that moves the electrons through the wire. Increasing voltage increases current (electron) flow.
To create voltage, magnets are used. The magnets strip electrons from atoms. As the electrons accumulate a negative charge builds. Likewise, the atoms with the missing electron accumulate on the other side and this becomes a positive charge.
In a battery, the - side of the battery is an accumulation of electrons. The + side is an accumulation of atoms with an electron missing. Electrons are strongly attracted to the atoms just as magnets attract. This is the magic that makes it all happen!
Amps (amperes) is a measurement of the flow of electrons in a wire, which is analogous to water's flow rate in a pipe like "gallons per minute". 1 Amp = 1 Coulomb (SI unit measurement of electric charge) x 1 Second. In the above battery for example, Amperage is a measurement of the electrons moving from the - terminal, through the motor or other device, to the + terminal. Once the atom and electron combine, the atom becomes neutral thus has no charge. As this migration continues, the voltage is steadily decreasing as the electrons rejoin their atoms.
Amps are defined as a certain number of electrons passing a given point in a given amount of time. (1 Amp = 6.24 x 10^18 electrons per second past a given point)
Watts , or the rate of power delivery. A watt is analogous to the energy or power like water in a watermill. If the same volume(amp) of water falls from a higher fall(volt) (like a 15 foot drop), it will produce more power than the same volume water from a lower fall (like a 3 foot drop).
Or use the analogy of water spraying out of a pipe onto the watermill paddle wheel. High volume low pressure will spin the mill paddle wheel as fast as low volume and high pressure.
So Watts are equal to volts x amps. To measure the total power (or gallons) delivered, you specify the power level and for how long - i.e. kilowatt-hours or total energy consumed.
Notice also that if you increase the pressure in the pipe (or voltage in the wire), the flow (current) will increase. Therefore, your power also increases. Put another way, if you increase the pressure (voltage), you can deliver more water (electricity) with a smaller pipe (wire). That's why electric power transmission over any distance is done at higher voltages, not at the much lower voltages typically seen by end
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