Short answers, pulled from the story.
The Books of Breathing are ancient Egyptian funerary texts intended to allow deceased people to continue existing in the afterlife. The word "breathing" in the title is metaphorical, representing all aspects of life the dead hoped to experience again. They are a simplified form of the Book of the Dead.
The earliest known copy of the Books of Breathing dates to around 350 BC. Copies continued to be produced through the Ptolemaic Kingdom and into Roman Egypt, as late as the 2nd century AD.
The original texts were titled "The Letter for Breathing Which Isis Made for Her Brother Osiris, The First Letter for Breathing" and "The Second Letter for Breathing". The letter framing tied the texts to the myth of Isis restoring the dead Osiris.
Some of the papyri that Joseph Smith (1805-1844) used to produce the Book of Abraham have been identified as parts of the Books of Breathing. This connection has made the ancient Egyptian texts a subject of ongoing scholarly discussion within Latter-day Saint studies.
The Books of Breathing are a simplified form of the Book of the Dead. Both texts served Egyptian funerary purposes, but the Books of Breathing offered a more condensed version of the ritual petitions to the gods on behalf of the deceased.
The Books of Breathing exhort various Egyptian gods to accept the deceased into their company. The texts function as divine petitions asking the gods to welcome the dead person rather than turn them away.