Dodge is a new mechanic introduced in XCOM 2, it gives a chance to receive a "grazed" shot taking only a portion of the damage. Unlike Aim or Will there is no natural way to increase Dodge; you will have to wear a Spider or Wraith suit or equip a Personal Combat Sim. However, in the War of the Chosen Expansion, soldiers can gain dodge as a bonus from some Covert Ops Missions.
Vipers, Codex, Archons and Elite Lancers come with a Dodge chance, you should take that into account when planning your strategies, especially if you plan to melee said enemies.
Explosives, psionics and other AoE attacks are not affected by Dodge; sometimes a Soul Fire or Combat protocol might be your best choice.
After a patch, shots from concealment and 100% shots aren't affected by Dodge either: Snipers with Bluescreen rounds can now reliably one-shot a Codex.