Well, it's a nice idiom really...despite its unfortunate origin.
Meaning & EtymologyEdit
To put someone out of their misery means - in the idomatic sense - to give someone good news, therefore stopping them from being miserable.
However, its origin is from when a suffering animal is put down (or 'put to sleep'), thus ending its suffering (so it is no longer miserable via illness).
Use in Normal SpeechEdit
When telling good news.
"Rosie put me out of my misery this morning - she's had a baby girl, Maya, and both are doing well. I was beginning to worry about her 'cos she hadn't phoned for days."
When telling of the passing of one who was suffering.
"Turned out Meg was worse than we thought...so we had no choice to agree to the vet putting the poor dog out of her misery."