Although I am not a "US friend", I'll try my best .
In the phrase, "class" is taken in the sense of group or category.
A class action is an action that is meant to settle a dispute affecting a large class of people in a similar situation, so as to avoid having multiple lawsuits with exactly the same issue. One single lawsuit can therefore resolve thousands of legal disputes in one go between a defendant and multiple individuals belonging to the same "class" or group of people being affected in the same or similar way by the action of the defendant.