부쳐주다 is composed of
부치다 means "send, post"
어 is a connecting particle
주다 is an auxiliary verb of meaning "do something for someone"
부쳐주다 means "send something for someone"
아빠가 저한테 돈 부쳐줬어요 means
My father sent money for me.
Quoted from http://www.howtostudykorean.com/unit-2-lower-intermediate-korean-grammar/unit-2-lessons-34-41/lesson-41/
Notice the difference between the two following sentences:
빨리 오세요 = Come quick
빨리 와 주세요 = Come quick (for me)
Notice that both sentences essentially have the same meaning. However, while the first sentence is simply a command, the second sentence (because of the nature of the word “주다”) implies that the desired action is beneficial to the speaker. Almost as if the action is a favor that the speaker would like to happen.
Therefore, adding ~아/어 주다 to a verb stem gives the sentence the meaning of “do __ for me.” This often translates more simply to “Please, …..” For example:
점심을 요리해 주세요! = Please, make me lunch
이 것을 만들어 주세요 = Please, make this for me
The two examples above have almost the same meaning as the following sentences.
점심을 요리하세요 = Make lunch
이 것을 만드세요 = Make this
Those two sets of sentences essentially have the same meaning. The only difference being that when using ‘주다’ you are specifically asking for some sort of ‘service.’ When you do not include ‘주다,’ you are just telling somebody to do something. However, by saying 주다, you are indicating that the person is doing something for you.
그 책을 제자리에 두세요 = Put that book back in its place
그 책을 제자리에 둬 주세요 = Please put that book back in its place (for me)