put to sleep

1.  Bore utterly, as in That show put me to sleep. This hyperbolic term implies that something is so dull one could fall asleep.
2.  Kill, especially as a kindness, as in We had to put the cat to sleep. This euphemism dates from the mid-1900s.
3.  Subject to anesthesia, as in This injection will put you to sleep so you won't feel any pain.

The verb has 3 meanings:

Meaning #1: help someone go to bed

Meaning #2: kill gently, as with an injection, as of pet animals
  Synonym: put away

Meaning #3: make unconscious by means of anesthetic drugs
  Synonyms: anesthetize, anaesthetize, anesthetise, anaesthetise, put under, put out