Corpses in war sometimes have horrible things done to them. Maybe a person died in a fire or got blown up or their head was blown off or something. This is the reason that soldiers in most armies wear identification tags (like the American "dog tags"), so that if they're killed in action and marred beyond recognition, you can take a look at their tags and go "Oh, so that's Smitty! Poor Smitty..."
However, sometimes the tags themselves are ruined or lost. In fact, it happens somewhat frequently depending on how a person died and where they died. So the casualty feeder card is keeping track of all of the casualties (aka wounded, dead, or captured soldiers). It gives the three options there, and then it gives two check boxes. One is for "Body Recovered". If you found a corpse, you can check that box "yes". The other is for "Body Identified". If you can figure out what whose corpse it IS, you check that box "yes". Sometimes a person will find a body but they don't know whose body it is, so they'll check BR with a "yes" and BI with a "no". And if a soldier is known to be captured, you'd check both boxes "no" because you obviously don't have the body.