An ampere is a measure of how many electrons move past a point every second (though technically, it's movement of any charged particles, but for metal wires it's always electrons). 1 ampere = 6,241,510,000,000,000,000 electrons per second. A pipe with water moving through it could be measured in gallons per second. Same idea.
Watts are not just used in electronics. They're a measure of the rate at which energy is used or transferred. A stick of dynamite and a candle have similar amounts of stored chemical energy, but the dynamite releases it much faster than the candle, so the dynamite has a higher power output (for a shorter time). Likewise you could use two identical batteries in different ways. If one way uses more power, the battery will not last as long.
1 horsepower is about 750 watts, if you're familiar with cars. Just different ways to measure the same thing.
watts = volts * amps. So a 60 W bulb plugged into a 120 V socket will be drawing 1/2 an amp.
60 W = 120 V * 0.5 A
In AC circuits, the electrons are vibrating back and forth instead of going in a continuous loop. The frequency is just the number of vibrations per second. 50 Hz means they move back and forth 50 times per second.
It's important to understand the difference between current flow and energy flow, though. The actual electrons in a wire don't move very fast. In a DC circuit, the actual electron flow around the loop might be at the speed of molasses. The reason flipping a switch causes the light to turn on very quickly is because the energy flow is very fast. The energy is carried by waves in the electrons, not the electrons themselves. They are constantly repelling each other, so when you push some extra electrons onto one end of a wire, the others nearby jump away, which causes more near them to jump away, and so on, creating a wave of "push" that travels down the wire and then pushes on things at the other end. This wave travels from one end of the wire to the other at maybe 2/3 the speed of light, while the electrons themselves barely move.
First of all you can control the voltage on the inverting input (-) in the range of 9 to 10V.
Opamp will try to keep the voltage on both its inputs the same by varying the output voltage. First assume that opamp is working in its linear region (output voltage is not saturated). This means the voltage on the non-inverting input (+) is exactly the same as the voltage on the inverting input.
If you set the voltage to 10V the voltage difference on the resistor R3 is 0V. Using Ohm's law this yields zero current. This also means there is 0A going through the load.
If you set the voltage to 9V the voltage on the R3 resistor is nor 1V (10V-9V). Using Ohm's law gives 1A. All this current is also going through the load (because opamp's input current is zero).
This way you can control the load current from 0 to 1A.
Now the dynamic behavior.
Assume you set 9.5V with the potentiometer. The voltage on the collector of the transistor is 9.5V. This means R3 voltage is 0.5V and load current is also 0.5A.
Now change the potentiometer to 9.6V. Opamp's inputs are not balanced any more. The inverting input's voltage is higher than the non-inverting input. Therefore opamp will adjust its output by lowering the voltage on the base of the transistor. The collector current will drop and so will the voltage on R3. V(R3) will drop to 0.4V at which point the input voltages will be equal and you will have a steady-state again.
Practical considerations.
Almost any opamp will work correctly in this circuit. You must consider maximal current opamp can give to the gate. If your output current is max. 1A, the gate current has to be 1A/(transformer beta). You must choose an opamp that will provide at least this much current.
You must also be aware that if you want your circuit to work when the output is shorted the voltage on the output has to go down to GND+0.7V. Even if it does not you can very easily correct it by adding a base resistor.
Best Answer
A very simple model for an opamp is used in the example below. A voltage-controlled voltage source with a gain of 1000 is used to build a non-inverting amplifier.
As you can see a difference of about 2mV is needed to get a voltage of about 2V at the output (since the gain is 1000). For a smaller difference at the input the output voltage is reduced and the voltage at the inverting input gets smaller. So it's actually the external negative feedback that takes care of a non-zero differential voltage and not the opamp itself. It just provides high gain.