Those die-hard fans of the sci-fi genre will likely recognize that a Babel fish is a device used in The Hitchhiker's Guide to The Galaxy, to translate directly from mouth to ear across several languages. The device takes words from one dialect and turns them into the native speakers so that they can be understood. This is an unusual ability that the One Ring of power seems to also possess.
There are surprisingly few times across the entire trilogy in which a character actually puts on the ring. It is usually kept upon a magic chain around the ring bearers neck to avoid skin-to-skin contact, as this makes it easier to keep hidden from the enemy. However, when the brave heroes do find themselves forced to put on the cursed object in times of great danger and necessity, it has the strange ability to heighten their senses, and make strange dialects from various creatures understandable to the wearer. However, as the ring slips the wearer into a sort of shadow realm, where it can cast out and seek for its true master, the gift only seems to apply to translating servants of the evil lord himself, and wouldn’t be any use in understanding elvish, or any of the dwarven or the Rohirrim languages.
The first time this strange effect takes place is in The Hobbit book, and equally so in the Peter Jackson film adaptation. When Bilbo and the thirteen dwarves are traveling through the elven realm of Mirkwood, they begin to realize that things are not as they seem and that their situation is actually quite precarious. In a state of almost drugged stupidity, they are set upon by a group of giant spiders, who are descendants of Shelob the spider demon.
The spiders capture the dwarves, led by Thorin, who has always been opposed to Bilbo, and string them up in their webs, stinging them into unconsciousness. Luckily, Bilbo is able to avoid this fate because he puts on the ring and disappears out of view. But when he wears the ring, the chittering noises that the arachnids were making suddenly turns into clear voices. He hears the talking plainly, in words that he can understand, although they are clearly not speaking the common tongue, but some archaic form of language. He hears them say “Now we see you, you nasty little creature! We will eat you and leave your bones and skin hanging on a tree.” The spiders, who have bad eyesight anyway, can actually see him more clearly in this weird, shadow-like realm that the ring puts people into.
Many, many years later, the ring has come to Frodo, and he has undertaken the quest to destroy it in the fires of Mount Doom where it was forged, alongside the fellowship who set out with him from Rivendell. The group has been separated, and all that remains is his brave companion Sam, and the creature Gollum who is leading them to their doom. After the two have climbed the steep stairs to Cirith Ungol, they enter Shelob's lair, where they are separated from one another. Unfortunately, Frodo is stung by the giant spider demon, and Sam believes him to be dead. Poor Sam takes the ring in order to destroy it, but when he places it upon his finger to escape some orcs who are roaming on guard duty, he is suddenly able to understand their conversation. Just as Bilbo could hear each word of the spiders, Sam can so hear the orcs.
In the book, it is described that "perhaps the Ring gave understanding of tongues, or simply understanding of servants of Sauron it’s maker, so that if he gave heed, he understood and translated the thought to himself." Perhaps this is a sort of spell or device that the dark lord placed within the ring when he tricked Celebrimbor, the elven smith, the better to understand and spy upon his enemies. But it in fact backfires, because the gift instead is used to the advantage of those who would choose to oppose him, and destroy the ring for the good of all. Without this strange ability, Bilbo may not have been able to survive the spiders, and Sam would never have known that Frodo was still alive, and needed rescuing from the orcs who had taken him captive.
It is also worth noting though, that the only two people who are ever recorded as noticing this 'Babel Effect' from the ring are both hobbits, so perhaps it was something that Sauron never intended, and the ring was just acting upon the powers of the creatures who wore it, as hobbits are known far and wide to be particularly good with language, words, and games like riddles, which all require a complex understanding of speech.