This is the 3734th most frequent Catalan word.
adormir
"Adormir" means "to put to sleep" or "to fall asleep" in English.
Here, 'adormir' is used to indicate the action of causing someone (the baby) to fall asleep.
Vaig adormir el nadó després d'un llarg passeig.
I put the baby to sleep after a long walk.
In this context, 'adormir-me' means 'to fall asleep', describing the subject's (my) unintentional entering into the state of sleep.
Quan la màgia em va tocar, vaig adormir-me sense poder evitar-ho.
When the magic touched me, I fell asleep without being able to avoid it.
The phrase 'adormir amb' expresses the act of falling asleep in a particular situation (with background music).