Do I need to bring a dictionary to class tomorrow?
Literal
Tomorrow [possessive-の] class [to-に] dictionary [object-を] bring-come necessity [subject-が] exist?
持ってくる ('bring') is 持つ + 来る — 'carry and come.' 必要がありますか ('is there a necessity?') is a formal way to ask 'do I need to?' The question structure nests a purpose (bringing) inside an existence query (is there a need?).