VERB (て form) + くれる is an expression that means "(you) do (that action) for me".
It's used to describe a speaker's modesty and appreciation for what a person (listener) is doing in consideration for(or for the sake of) the speaker.
In a sense, Nourman Hajar's interpretation is correct, as the listener is giving (bothers to do) an action for the sake of the speaker.
For example:
お母さん、育ててくれて、ありがとう。
(Thank you for raising me, mother.) = the action of 育てる is done by the mother for the speaker.
お父さんが、おみやげを買ってきてくれた。
(My father bought souvenir for me./My father bothered to buy souvenir for me.) = the action of おみやげを買う is done by my father for the speaker.
明日、休みを取ってくれると、うれしいな。
(I'll be happy if you take a day off tomorrow for me.) = the action of 休みを取る will be done for the speaker's wish. (+ this one has a conditional sentence structure that describes the speaker's wish.)
The emphasis (of appreciation or the feeling of the speaker) is placed on the DOER of the action. This is the same concept as the verb くれる.
(In the same manner, there is also "VERB (て form) + もらう" to describe YOU received the service (action) by bothering the doer.)
Hope this will help. :)