Googles definition of Mitigation is: "the action of reducing the severity, seriousness, or painfulness of something." In other words its how much of the damage you take is reduced by your defensive capabilities such as blocking, armor and abilities.

proc is a when something that has only a small precentage of happening happens. Say you have the Nerien'eth set, its has a 10% chance when casing non Damage over Time Damage to spawn a Lich Crystal that deals area of effect damage. When said crystal spawns you say that it has "proc'ed"

I hope that answers your questions and if you want to know more about Mitigation I made a post about it here: forums.elderscrollsonline.com/en/discussion/187110/dmg-mitigation-for-tanks