Mother sent me a birthday present.

Literal

Mother [subject-が] birthday [gen-の] present [obj-を] sent-for-me.

Straightforward ~てくれた sentence. The only thing of note is that 誕生日 (birthday) is a relatively formal/neutral word — casual speech might use バースデー (borrowing) or お誕生日 (politer). Notice the absence of a recipient に: it's implied by ~てくれる that the speaker is the receiver.