A poor relation is, literally, someone who is a relative and is poor, but it generally has the connotation that the person or thing so referenced is an inferior or less worthy member of the family or group. I don't know what an appositive is, but the general meaning of the sentence is that she gave a wonderful present to you, even though you might not ordinarily be considered worthy of her notice.
So, "a poor relation" equals "me." Appositive is put to a word or phrase to add additional information. In this case "a poor relation" is an appositive to add additional info to "me."
Thank you Artemis!