A terrist is a radical environmentalist or a self-proclaimed green anarchist who sees her or him self as heroically defending the Earth, or "Terra" (Latin), from humans or other forces acting through humans - typically ideologies or technologies, which they see as out of control. They may or may not profess the 'Earth immune system' ideology of Gaians.
There is so far no openly stated ideology called "terrism". That may be deliberate, as terrists usually see it as unnecessary to discuss, explain or agree. Instead they act.
Many terrists oppose capitalism as inherently dirty and destructive of the natural world. Others view technology as the enemy, and some state that they seek human extinction, e.g. through suicide, cannibalism, abortion, euthanasia, and other means. A notable group of this sort is the Church of Euthanasia. Some consider the Anarchist Golfing Association to also be taking a basically terrist position, as they offer a relatively weak rationale for attacking the game of golf, itself a symbol of what they oppose. Both groups might also reasonably be called situationist.
Critics of such groups often consider them insincere or mentally unbalanced, and believe that extreme goals and visible actions are nothing but a publicity stunt. As evidence they point to the fact that the term "terrist" was openly coined in deliberate mockery of the term terrorist, which is sometimes pronounced (especially with certain American accents) as "terrist". A web search will verify that this is the most common use.
Radical environmentalists don't usually openly state that they are terrists, but seek some socially acceptable rationale for their actions. As with the word "terrorist", if someone says they are a terrist, they probably aren't, but are just seeking publicity.