basically, pretty much almost everything you do in BP is playing with object reference (the blue variable). an object reference is an instance, refering to an actor instance in your scene or somewhere else. class reference (the purple variable), you can see these purple when you want to create an instance from a class(those BP in your content browser).
If you want to save reference as variable, you just drag out the blue line and hit promote to variable, then you can access the reference from somewhere else. For a chessgame, each pawn is an instance, you need to decide which one you are moving with your controller, maybe a trace from your mouse cursor, get the hit actor and modify it.