Canned and jarred goods are cool. The word "processed" can refer to a wide range of things. What we mean by processed is anything that wasn't achieved by standard, traditional cooking means.
If your tomatoes, for instance, are just peeled and crushed, or even made into tomato sauce by cooking, it's all good. You'll want to look at ingredients to be sure there aren't any non-compliant ones. Anything that is used to stabilize, extend shelf life, etcetera, is what "processed" means in the Whole Life Challenge. Think "artificial" and you may get a better idea.