The SRESS CARD is a card issued to new Army trainees that they are to keep in their shirt pocket. Any time they feel that the mean Drill Sergeant is pushing them too hard, the trainee takes out the card, and must be given a break to collect themselves.
Four Drill Sergeants are screaming at Private Snookems because he forgot to bring his entrenching tool (again). Snookems is feeling a bit crowded, and can't take all this stress... those Drill Sergeants are just too mean. So he takes out his STRESS CARD and like magic, the pressure goes away.
Too bad he can't use a STESS CARD in combat, though.