Dog tags are tags worn by army personnel used to identify a persons body if killed in action or for medical details like blood type if in need of treatment. They are usually made from metal in the shape of oblongs (though they can be circles) with names, date of birth, blood type and regiment in the army etched onto it. There are two tags per soldier, so one can be broken easily to make gathering records of who has died easier and quicker since trying to carry the whole chain and other tag would be inconvenient while the other is left for personal identity.
They were constanly seen and mentioned in the film like when Captain Miller removed Carparzo's tags and when Lieutenant Dewindt handed Miller a bag of dog tags. They are not bullet proof, however, proven by how Private Reiben commented on a soldiers dog tag saying "look at this poor bastard" referring to a bullet hole with blood around it.