Legendary Items are magic items which grow in power as their wielder grows. What may be a common +1 weapon at first level might become a +4 wounding blade with several magical powers by the end of the wielder’s career.
Legendary Items aren’t restricted to weapons. Cloaks, bracers, amulets, and other wearable items have been known to be Legendary. Less common are items such as carpets, books, and chests. There are rumors of Legendary Armors, but none confirmed. Shields are relatively common.
One known Legendary Item is the Stargazer.
In game terms, to attune a Legendary Item to yourself requires some combination of minimum skill levels and a feat or class ability. Anyone meeting the requirements by fourth level will create a bond with the item and advance it to its second level of abilities. Every two levels after that, the items advances one level. Items that aren’t weapons or shields don’t have as many levels; the requirements are needed by fifth level and advance every five levels.
Most information about Legendary Items comes from Purple Duck Games ‘Legendary’ series of Pathfinder supplements.