It's all about the temperature/pressure relationship, and how pressure affects the boiling point of the refrigerant. As the pressure of a refrigerant goes up, so too does the temperature and boiling point. When the pressure drops, the temperature and boiling point drop as well. Air conditioning (and some heating) systems take advantage of this, to cool (heat) the air inside a building.
Normal system
In a normal system, The compressor compresses the refrigerant vapor. This causes the vapor to be both high temperature, and high pressure. The hot vapor moves through the condenser coils, where some of the heat is transferred into the outside air. When the vapor finally comes out of the condenser, it's a hot liquid. The hot liquid moves through the liquid line, into the building towards the evaporator coils. Just before the hot liquid refrigerant reaches the evaporator, it's forced through a metering device. The actual device used depends on the system, but capillary tubes are common.
When the hot liquid is forced through the metering device, the pressure drops substantially. The pressure drop causes the temperature and boiling point of the liquid to also drop. As indoor air is forced over the evaporator coils, the cold liquid refrigerant in the coils absorbs heat from the air. The heat causes the refrigerant to boil, which changes it to a low pressure vapor. When the refrigerant reaches the end of the evaporator, it's a cool vapor. The cool vapor travels down the suction line, and back to the compressor where the refrigeration cycle can start again.
Low refrigerant
When the refrigerant in the system is low, the pressure; and therefore temperature, of the refrigerant will also be lower. In a normal system, the temperature of the refrigerant at the beginning of the evaporator will be right around the freezing temperature of water (32°F). As the indoor air moves over the cool coils, the moisture in the air will condense on the coils. This condensation will drip harmlessly off the coils, and into the condensate drain.
When the refrigerant is low, the temperature of the refrigerant at the beginning of the evaporator coils will be colder than the freezing point of water (less than 32°F). Because the coils are so cold, the condensation that forms on the coils will freeze. As ice builds up on the coils, it restricts the air flow through the coils. Because of the restriction, the refrigerant can't absorb as much heat from the the indoor air moving over the coils. This causes the refrigerant to boil later in the evaporator, which causes ice to form further along the coils. This situation continues to progress, until the whole evaporator is a block of ice. Once that happens, the refrigerant will start to boil in the suction line. This cause the temperature of the suction line to drop, and just like in the evaporator, cause the condensation to freeze.
Eventually the freezing works its way all the way back to the compressor, which is where the trouble can really start. If allowed to operate in this condition for too long, liquid refrigerant can make its way back to the compressor. If this happens, the compressor can be damaged.
It should also be noted. Once the refrigerant level drops too low, the system stops working. So this problem only occurs in a "sweet spot", where the refrigerant is low, but not too low.
Best Answer
Chlorodifluoromethane, also known as R22 refrigerant has a boiling point of -40°F at 0 psi. As you increase the pressure of the refrigerant, the boiling point also increases. At 68.5 psi, the boiling point of R22 is 40°F.
In a normally functioning system, the refrigerant is sent into the evaporator at about 55-65 psi. Which means that the boiling point will be above the freezing temperature of water. The refrigerant absorbs heat from the air passing through the evaporator, boils, and flows on down the line at a temperature above the freezing point of water. The refrigerant will likely be below the dew point, however, so there will be condensation on the line.
If the pressure in the system drops, the R22 might be entering the evaporator a bit lower than the typical pressure. In this case, the boiling point of the R22 will be below the freezing temperature of water. As the warm moist air moves over the evaporator, the moisture condenses and freezes on the coils. Ice will start to form at the beginning of the evaporator coils, and slowly creep along its length.
The ice will act as an insulator, so the refrigerant in the line will not be able to absorb the heat it needs to boil. This causes the refrigerant to boil off further along in the evaporator, which forms more ice further down the line. This process continues all the way along the line, until the entire evaporator and suction line are covered in ice.
Once the refrigerant levels get too low, there's not enough refrigerant in the system to freeze the line. So eventually if the system has a leak, this behavior will stop and you'll simply get no cooling at all from the system.
NOTE: I could be completely wrong here. This is based on my limited knowledge of air conditioning systems. I am not an expert in thermodynamics, fluid dynamics, chemistry, or HVAC.