This is the 5341st most frequent Russian word.
отдавать
To give back, to return, or to give away.
The verb 'отдавать' here means 'to give back' or 'to transfer something to someone as a gesture of goodwill, completing an action of giving.'
Я отдаю другу свою книгу.
I am giving my book to my friend.
Here, 'отдавать' is used in the sense of 'to devote' or 'to allocate something non-material such as time or effort to something else.'
Он отдаёт много времени работе.
He devotes a lot of time to work.
In this context, 'отдавать' signifies the action of officially transferring someone to the care or responsibility of an institution or another person.