When the evaporator coil is dirty, your air conditioner will not generate air that is as chilly as it should be. A very filthy evaporator coil might cause your air conditioner to fail entirely.
Another sign of a problem is if your air conditioner starts running for longer cycles to provide the same level of cooling in your house. When the air it generates isn't as cold, it has to create more air to lower the temperature in your home to the desired level. If you see this, the evaporator coil might be to blame.