R.A.B. – Harry Potter Lexicon

"That was Sirius’s brother, wasn’t it? Regulus Arcturus . . . Regulus . . . R.A.B.! The locket—"
-- Ron Weasley (DH10)

The initials of Regulus Arcturus Black, brother of Sirius Black, used as a signature on a note to the Dark Lord.

Harry and Dumbledore apparated to the sea cave where Voldemort had once hidden Slytherin's Horcrux Locket in a basin of poisonous potion (HBP26). After Dumbledore drank the potion, they flew back to Hogwarts where Dumbledore met his death on top of the Astronomy Tower. A battle ensued, but later Harry found the locket in Dumbledore's pocket, and inside was the note signed "R.A.B." (HBP28).
Harry did not know the true identity of R.A.B. until he, Hermione, and Ron were forced to hide at Twelve Grimmauld Place and Harry entered the room of Sirius's brother, Regulus Black (DH9).
The House-elf Kreacher had been forced to go to the cave with Voldemort so he could hide Slytherin's Locket in the first place, and the Dark Lord left Kreacher to die. But he was able to survive the Inferi in the water using House-elf magic and find his way home, where Regulus was shocked to hear the way Voldemort had tossed the elf away when he wasn't needed anymore (DH10).
Regulus also realized why the Locket was important, that it was a Horcrux holding a soul-bit from Voldemort that would make him survive death, so he decided to go back to the cave with Kreacher and replace the real locket with a decoy and his note. Kreacher survived to bring the real locket back home with him, but Regulus drank the evil potion and was pulled under the water by Inferi (DH10).
Harry allowed Kreacher to keep R.A.B.'s fake locket, which he wore at the Battle of Hogwarts while shouting "Fight! Fight! Fight for my Master, defender of the house-elves! Fight the Dark Lord, in the name of brave Regulus! Fight!” (DH36).
Kreacher helped Harry track down the real Horcrux Locket, which was stolen from Grimmauld Place by Mundungus Fletcher and sold to Dolores Umbridge (DH11, DH13). It was later destroyed by Ron Weasley using the Sword of Gryffindor (DH19).