The purpose of all HVAC/R coils is to transfer heat from one medium to another through the walls of the tubing. Metals like copper or aluminum are often used for coils because they have good thermal conductivity, which means heat moves through them easily. When coils get a coating of dirt on them, it can act as thermal insulation on the metal impeding the movement of heat in and out of the coil.
Therefore, because heat moves from higher temperature to lower temperature through materials via conduction any material on the coil (like dirt) with lower thermal conductivity and higher R-value results in lower heat transfer and therefore some potential performance impact on system performance.
When dirt and other contaminants block coil fins, it causes a more substantial air pressure drop across the coil, which results in either lower airflow over the coil or higher power consumption on the motor depending on the motor and fan type. Buildup of dirt can slow down AC fans which increases in air resistance also. As the coil gets dirtier, the motor moves less air, resulting in less heat transfer and lower efficiency.
Performance & Capacity
When coils get dirty, the amount of heat the system can move tends to decrease. Often, your appliance will need to work at full capacity during times of high load, and this is the very moment when dirty coils tend to cause the most significant issue; The primary one being air circulation and heat transfer.
Like most appliances and systems, when they are dirty it results in more friction and the system having to overwork to compensate for the blockage. By keeping the coils clean, the systems work load is reduced and thus lifespan increased.