An ancient mineral used to craft a mighty blade.
Dreamstone is an ancient mineral colored crimson that was once valued above gold in antiquity; in 65000000 B.C., it is prized by the people of Ioka as a symbol of leadership. Naturally occurring in the planet, Dreamstone is an exceptional conductor of the elemental energy of Lavos, even able to channel it for external use and store it for periods of time. It may be capable of channeling energy or magic well in general. The position of chief over Ioka included guarding a piece of the rock; later, in Zeal, it was kept as a royal family heirloom. After the power of Lavos was discovered, the Mammon Machine was constructed using Dreamstone, as well as the Masamune and Pendant by the Gurus of Zeal. Through the Mammon Machine, Zeal was able to tap the infinite reserves of power below, prompting the construction of the Ocean Palace to siphon even more power. Meanwhile, Sealed Doors were created throughout the magical kingdom that could only be opened by a pendant charged with energy from the Mammon Machine.
After the Fall of Zeal, the Dreamstone of the royal family of Zeal apparently was destroyed or disappeared, as the mineral became impossible to find in later eras (only appearing in the form of the pendant around Marle's neck). This posed a problem when the Masamune required some for repairs; the party ventured millions of years in the past to obtain some from Ayla. Melchior demonstrated that the Dreamstone required processing to be used in blades and fine materials. The NA version of the game states that Dreamstone was used as money, but this is incorrect; Melchior merely states in the original that it was an ore valued above gold.
There is no appearance of Dreamstone in Chrono Cross, but Ultimania claims that the Frozen Flame and Dreamstone are one in the same. Masato Kato reiterated this stance (clarifying that Dreamstone also consists of shards of Lavos) at May 2022 - Chrono Cross Radical Dreamers Edition Questions and Answers, prior to the HD Remaster coming out, causing a plot inconsistency (see link in analysis section). Both Dreamstone and the Frozen Flame conduct Lavos's energy in a way, but it is most likely the Frozen Flame that is spoken of in Chrono Trigger's Zeal:
[Book] It all began aeons ago, when man's ancestors picked up a shard of a strange red rock... Its power, which was beyond human comprehension, cultivated dreams... In turn, love and hate were born... Only time will see how it all ends.
Emphasis is on "shard." While Dreamstone certainly is powerful, it was in possession by humans long before the creation of Zeal in varying amounts, apparently without expanding their mind like the passage states. The Frozen Flame, of course, is responsible for the abnormal growth of the human brain when it made contact with humans in 3000000 B.C., metaphorically "cultivating dreams," leading the apes out of the caves to create Zeal and begin modern civilization. The question becomes a matter of whether Masato Kato had planned the Frozen Flame's existence at the time of Chrono Trigger's completion.
One interesting possibility that would bring both Ultimania and the game's canon into union is that perhaps Lavos's shell, when formed on the planet he came from as a spawn, was actually made partly of Dreamstone, and that the Frozen Flame is simply a very special piece (with some kind of intelligence and functioning life system). This hasn't been confirmed anywhere, however. What appears to be Dreamstone as depicted in Trigger's art appears on a wall engraving in a cut scene taking place in Fort Dragonia; a human kneels in front of it. However, considering that in the same scenes a.) Lavos is modeled to be a giant, falling sun, b.) the Dragonians include the two moons in the history, though it did not exist until Dinopolis came around with Chronopolis, the Dragonians apparently had no idea what the Frozen Flame, Lavos, or other artifacts of the human world looked like. The apparent Dreamstone is thus probably a stylized rendition of the Frozen Flame, since the mural allegedly depicts the event of human modification in 3000000 B.C. through the Frozen Flame.