Final answer:
Microtubules are the cytoskeletal fibers responsible for moving materials within the cell and organizing the cytoplasm, providing cell structure, intracellular transportation, and facilitating cell division.
Step-by-step explanation:
The fibers of the cytoskeleton that move materials within the cell and organize the cytoplasm are called microtubules. Microtubules are the thickest fibers within the cytoskeleton and are comprised of polymers of alpha and beta-tubulin.
These hollow tubes provide structural support, enable intracellular transport of organelles, form the nuclear lamina, and are essential during cell division to pull chromosomes apart. Microtubules are also key components in the structure of flagella and cilia that facilitate cellular movement.
While microfilaments, composed of actin, are essential for muscle cell contraction and cellular motility in cells with microvilli and pseudopodia; and intermediate filaments, which vary in composition, provide structural integrity and organizes internal cell structures, the specific answer to the given question is microtubules.