Class 1 sensors have tighter defect classification than Class 2 sensors - typically fewer hot pixels, fewer bad columns, etc. Some sensors don't have multiple grades, e.g. KAF-16803 is only available in one standard grade. Others have Class 1 and Class 2. Some sensors from other manufacturers have multiple levels available. There is usually also an "engineering grade" option as well, which is a sensor that works but doesn't meet specifications. They are a lot less expensive but the manufacturers often limit quantities to one or two. They are intended to be used during camera design, rather than in products. The manufacturer charges a lot more for Class 1, which is why the cameras are more expensive.
Usually professional research applications (professional astronomers, research projects, science instruments) or experienced astrophotographers want Class 1 sensors; People who are doing casual imaging are usually very happy with Class 2. Also, sometimes "Class 1" is referred to as "Grade 1".