Harry, Ron, and Hermione have no idea what "the Deathly Hallows" means. Xenophilius says that the symbol isn't Dark, and asks if they're familiar with "The Tale of the Three Brothers." Only Ron is, and Hermione pulls out the book from Dumbledore to read it out loud. It tells the story of three brothers who meet Death at a bridge. Death offers them prizes when they don't die in the river. The oldest asks for a powerful wand and the second asks for the power to recall others from the dead. Death fulfills these requests. The youngest asks for something that will allow Death to not follow him, so Death hands over his own Invisibility Cloak.
Giving Ron this opportunity to know something that neither Harry nor Hermione do allows Ron to continue to build himself up again and feel like he's an integral part of the group, not a guilty straggler. The gifts that the brothers ask for show another way of attaining immortality by thwarting death, which introduces Harry to the idea that immortality isn't only attainable through Horcruxes.
The first brother boasts about his wand and another wizard kills him and takes it. The second brother brings his long-dead lover back to life, but she's unhappy and he commits suicide to join her. The third brother lives a long time and gives the cloak to his son before following Death to his own death. Xenophilius picks up a quill and draws the Deathly Hallows—the Elder Wand, the Resurrection Stone, and the Invisibility Cloak—into the triangular symbol. He says that having all the objects will make a person the master of death. Hermione is skeptical that they exist. Xenophilius says that the Cloak is different from others in that it doesn't fade, and Harry thinks his cloak is like that. The evidence for the Resurrection Stone is spotty, but Hermione doesn't contradict that history shows signs of a single wand changing hands violently.
The fates of the first two brothers suggest that immortality, whether through Hallows or through Horcruxes, is still not a worthy goal: a better goal is to emulate the third brother and seek to die on one's own terms, while also protecting and preparing one's children for death on their own terms. It's also worth keeping in mind that black elder—presumably, the wood used in the Elder Wand—is poisonous, which suggests that the wand itself is dangerous because of its materials. This is supported by the fact that Voldemort's wand is yew, which is also extremely toxic.
Hermione asks if the Peverell family is related to the Hallows. She says she saw the symbol on a grave in Godric's Hollow, and Xenophilius says that the Peverell brothers were the original owners of the Hallows. He invites the trio to stay for dinner and heads downstairs. Hermione sighs that the Hallows are rubbish and the story is just a morality tale. They all say which Hallows they'd choose and debate their merits, and Ron points out that Harry's Cloak really is different from others. Harry walks around and discovers that the stairs lead to Luna's room. There, he finds a mural of him, Ron, Hermione, Ginny, and Neville painted on the ceiling, with "friends" written all around them. The room, however, is dusty and it looks like Luna hasn't been home.
Luna's mural reminds Harry that there are definitely others out there who care about him and who will happily dedicate themselves to the cause. However, seeing this reminder in the form of the mural and also realizing that Luna isn't around suggests to Harry that Xenophilius isn't actually here to help them. This reminds the trio again that they need to be careful who they trust, as they have enemies everywhere in addition to having friends everywhere.
Xenophilius returns with four soup bowls and won't answer Harry when he asks where Luna is. The printing press emits a bang and shoots out several Quibblers. Hermione picks one up. Harry is on the cover, "Undesirable Number One" printed under his photo. Xenophilius whispers that the Death Eaters took Luna and might give her back if he hands over Harry. Hermione spots Death Eaters outside as Xenophilius tries to Stun them and hits the Erumpent horn instead. The room explodes and Xenophilius falls down the stairs. Harry finds Hermione and they hear two Death Eaters taunting Xenophilius downstairs. One of them sends Xenophilius up to bring Harry down—or they'll kill Luna.
Xenophilius's behavior here reminds Harry and the reader that being good or bad is more complicated than the binary might suggest. Xenophilius isn't a bad person, but in order to keep his daughter safe, he's being forced into doing some horrible and questionable things—things that he might believe are worth it if Luna survives. This will help Harry to develop a sense of empathy, as well as a greater sense of caution.
Harry and Hermione quietly dig Ron out. Hermione makes Ron put on the Cloak and when they see Xenophilius's face, she shoots a Memory charm at him, blasts them through the floor so they see the Death Eaters, and then they Disapparate.
Hermione clearly has a plan as they escape the Lovegood's home, which reminds Harry again that he needs his friends and all they bring to the table in order to stay safe.