I think it's pith, but here (non-english country) many chef suggest orange's vascular veins which look "fibrous" and have similar translated word with "fiber" itself. Please enlighten me which?
Cellulose is one of the most common sources of fiber in the nutritional sense. Because oranges are plants, their cells have cell walls, made out of cellulose, so some of the fiber in an orange is surrounding each individual cell. Both vascular cells and pith cells tend to have particularly thick cell walls, so they are probably higher in fiber (this article also suggests that the pith is particularly high in fiber - vascular tissue is probably not mentioned because it is less prominent).