Oku is used like that (after the te form of the verb) to indicate setting things up and then leaving them set up like that, often in preparation for some future contingency. Literally it's the oku that means "to put" - it's like you are putting something in its proper place to be ready for later developments.
I'll post in a bit from a dictionary, hope the copyright is OK. You can see that it's always setting up a state of affairs that will then remain constant for a certain period of time.
2 〔「窶ヲしておく」の形で〕(1)〔前もってする〕
お部屋を掃除しておきました I've cleaned the room for you.
彼が席を取っておいてくれた〔確保してくれた〕He 「has kept [has saved / 〔予約してくれた〕has reserved] a seat for me.(2)〔そのままの状態にする〕leave;〔させておく〕let 《a person do》
ドアを開けっ放しにしておく leave the door open
そのままにしておけ Leave things as they are. / 〔触れるな〕 Leave it alone.
混ぜたら一晩そのままにしておきなさい After you mix it, let it stand overnight.
言いたいことを言わせておいた I let her have her say.
彼を長い間待たせておいた I kept him waiting for a long time.
部屋の温度を一年中一定にしておく必要がある.The room temperature has to be constant all the year round.(3)〔さしあたりそうする〕
聞かなかったことにしておこう I'll just pretend I didn't hear it. / I will say I have not heard about it.
お礼の気持ちだから取っておいてください Just accept it as a token of my gratitude.
Progressive Japanese-English Dictionary, Second edition (c) Shogakukan 1993.