Wearing mithril armour is sometimes useful as it is the lightest metal armour. This means that the player has somewhat decent protection for general purpose exploring while being able to run longer than if they were wearing higher class armour.
Mithril is the only metal that has different level requirements for mining (level 55) and smelting (level 50).
Mithril was created by J.R.R. Tolkien, the author of the Lord of the Rings, amongst other works. Since its creation, though, mithril has become a metal found commonly in fantasy games.
Third age warrior armour examine says: "Fabulously rare armour beaten from magical silver" referring to the section above and might mean that Jagex wanted to use "mithril" but this term existed already in the game.
In Lord of the Rings, mithril is "light as a feather" and "stronger than forged steel". In Runescape, Mithril is one of the lightest types of metallic armour, yet a significant step up from steel in terms of protection.