A few things we need to know before we begin are that first and foremost, temperature and pressure are closely related. As temperature rises so does pressure, as pressure rises so does temperature. The second point is regarding the curved line on the diagram. This is know as the saturation curve and refers to the state of the refrigerant. Refrigerant has two possible states which are vapor or gas, and liquid. It is enough to know for this discussion that the area area inside the curved line is a blend of vapor and liquid with somewhere between 0-100% of liquid. The area outside of the curve is pure vapor.
Expansion is most easily understood as a method of rapidly decreasing pressure. This can be achieved by simply increasing the size of the copper tube that the refrigerant is travelling in at the point you wish to decrease pressure. In practice this is a precise and often complicated process. Expansion decreases the pressure and temperature of the refrigerant before it enters the evaporator in a low pressure/low temperature state (usually around 6 degrees Celsius). This is where the cooling begins. The warm air inside your home is then pulled across the coils containing the cool refrigerant and the heat is transferred into the much cooler refrigerant. The cooled air (usually 12-16 degrees) is then returned to the room much to the appreciation of the occupants. The refrigerant then continues on to the compressor and the cycle commences again.
More technical - COP and EER
One of the energy star ratings you will find on a new air conditioner for heating is determined by the "COP". This is literally the coefficient of performance. There are ways of calculating this figure using energy consumption however the method I've always used is using the diagram above. If we look at the evaporator line from the left at (5) until the point at which the saturation curve intersects, this is known as the 'refrigeration effect'. The line between the compressor (1) and the top of the compression cycle (2) is called the heat of compression. To get these figure simply measure the temperature in degrees at each point and determine the respective temperature ranges. If we divide the refrigeration effect by the heat of compression we are left with the COP.
The other energy star rating you will see relates to cooling mode and is known as EER or Energy Efficiency Ratio. This is simply the amount of output energy divided by the input energy. For example if you have a 6KW unit and the input rating is 1.5KW then your EER is 4. The figures to calculate the EER are usually available on the appliance sticker or nameplate on the outdoor unit.
Even more technical
The small area on the evaporator line that precedes the compressor is known as the suction super heat or SSH. This ensures that any refrigerant that enters the compressor is not in liquid state as this would likely destroy the compressor. The standard SSH is 6-7 degrees Celsius. You may also notice that the diagram shows the refrigerant to be a vapor when entering the expansion stage. In practice this not the case as expansion devices are much more stable when the refrigerant is a liquid.
Remember...only a fully qualified air conditioning and refrigeration tradesman understands your air conditioner.