As of December 9th, 2017 Ashe has featured on the free champion rotation more than any other champion at 76 times.
Ashe is likely based on Guinsoo's DotA character, Traxex the Drow Ranger.
Both share very similar visual and gameplay designs, such as being played as marksmen in their respective games and the ability to shoot ice arrows to slow down opponents.
Ashe's True Ice bow belonged to her ancestor Avarosa, the ancient Iceborn queen of unified Freljord.
If Ashe, Sejuani, and/or Lissandra find themselves in the same match and in opposing teams, Battle for Freljord will trigger. This in-game quest consists in one killing the other to earn the title of 'Queen of Freljord' (complete with a floating ice crown floating above their heads) referencing the civil war taking place there, between the three tribes each lead.
Amethyst is a violet variety of Quartz, often used in jewelry. It is known as a meditative and calming stone which works in the emotional, spiritual, and physical planes to provide calm, balance, patience, and peace.
This fits perfectly Ashe's goals of peace, unification, and prosperity for the Freljord.
The Avarosan (led by Ashe) are allied with the Frostguard (led by Lissandra) and engaged in a civil war with the Winter's Claw (led by Sejuani) over sovereignty of the Freljord.
Unbeknownst to all, Lissandra is the Ice Witch of Freljordian legend, who is actually waiting for the right moment to betray Ashe and destroy both hers and Sejuani's tribes in order to take over the Freljord and prepare for the Frozen Watchers' return.
As revealed by Lissandra, she herself is one of the Three Sisters who led the Iceborn uprising against the Watchers. Whether or not she knows Ashe and Sejuani are direct descendants of her sisters (Avarosa and Serylda, respectively) making her their great-aunt-many-times-removed is unknown.
Evidence to support Ashe's heritage stems from Ezreal's uncle Lyte stating her 'striking resemblance' to Avarosa herself, as well as the fact Ashe was coincidentally led to Avarosa's grave by a great hawk and recovered her ancestor's True Ice bow she carries with her to this day.
Ashe is close friends with Anivia and Nunu (and by extension Willump) All of them support her and the Avarosan's goal of peace and unification. Gragas is another supporter.
If the Avarosan win the war and both Ashe and Tryndamere become the new royal family, the boy and his Yeti partner will be appointed the Freljord's emissaries, and the Rabblerouser will struck a business partnership with them by being sold ownership rights of Freljord's Avarosa Iceflow Glacier (possibly in thanks for him helping the Avarosan settle matters with a smaller tribe by getting everyone drunk and drowning their troubles away)
Whether the new regents will marry strictly for political reasons or not is uncertain. All references to their relationship were removed in V3.6 due to the Freljord event also rewriting many champions' main lore.