if something is put to sleep, it is killed. you say "put to sleep" to your baby sister, or when you feel like shit and don't want to start crying until you have a shoulder to lean on. this term is generally used wrt animals (yea yea people are animals who gives a shit), and people may be offended if you use it wrt humans, because that's what the nazis did (after torturing the people and making them work as slaves for a while, of course).