Used when any choice among a set is acceptable or will do. Often implies indifference or that all options are equally fine.
See also: どれ
You can choose whichever one you like.
Any of the drinks is fine with me.
Please take any one from these.
Please choose whichever book you like from these.
I don't mind which seat I get.
どれ is the plain interrogative 'which one?', while どれでも adds でも to mean 'any one, whichever' with no question intended.
Compound of どれ (interrogative 'which') + でも (particle meaning 'even' or 'any'). The combination yields the meaning 'any one' or 'whichever'.