Contextually means “in a way that belongs to the situation around something.” If a word is contextually right, it fits this setting, even if it would sound odd somewhere else. “Contextually, this makes sense” means: if you look at the situation, the pieces hang together. Same school-and-essay flavour as contextual. You will meet it in papers and talks more than from a friend on the phone. In everyday English, “in this situation” or “in context” does the same job with lighter words.

就脈絡而言、在該情境中。和 contextual 一樣，偏書面、課堂用語。