Gauntlet is "the other PVP". Here you will need to go as high as possible in stages, and ranking will be less important than in arena.
Gauntlet goes in seasons. The season lasts a couple months and showcases a featured toon. Charlotte was the previous target, now we have the ancient mariner. Fragments for those toons will drop from gauntlet related events and will be available in gauntlet specialty packs.
Each gauntlet stage bears a certain number of battles. Beat all those battles and you'll progress to the next stage.
You can't reuse toons you've previously used in this stage. This mean that a 2 battle gauntet stage will need 2 eddies and 6 allies to complete. This goes on so a 6 battle stage will require at least 6 eddies and 36 allies.
Each stage can have additional stipulations such as (but not limited to) :
Reaching high gauntlet stages will provide you with fragments of Final Frontier Eddie, fragments of the specialty toon, other fragments (usually heroics) and rare talismans.
The highest gauntlet stage (SSS) is recurring, meaning if you beat it, you stay in SSS but get a better rank for winning. Also your toons don't reset between SSS stages (you can't use the ones you used on the previous SSS run).
You get IC for playing gauntlet, stage F will provide similar amounts as arena, but as you get higher the rewards increase. AA gives more than 50 IC for each battle.
Gauntlet resets every two weeks, so bear that in mind to plan your battles.
A few advices on gauntlet :