It is critically important to distinguish between what is necessary and what is not.
Literal
Necessary things [and-と] necessary-not things [object-を] distinguishing [topic-のが] extremely important [copula-である].
見分ける means 'to distinguish, to tell apart.' ことがきわめて重要である uses きわめて ('extremely') with the formal copula. A philosophical/practical observation about judgment.