The commas in the sentence "My brother, who lives out of town, will visit this Christmas" serve to set off a non-restrictive (or non-defining) clause. The clause "who lives out of town" provides additional information about "my brother," but it is not essential to the main meaning of the sentence.
If you removed the clause and the commas, the sentence would still be complete and clear: "My brother will visit this Christmas." The commas indicate that the information in the clause is supplementary, and the sentence would still make sense without it.
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