The spindle apparatus, or simply the spindle, is a network of microtubules (also called "spindle fibers") that forms within a dividing eukaryotic cell, both during mitosis and meiosis (see upper image at right). Some of these microtubules attach to the cell walls, others attach to individual chromosomes at their kinetochores.
It's the spindle that pulls the chromosomes from the metaphase plate to the poles. The radiating microtubules of the spindle form asters (see lower image, right) — aster is Greek for star. The two points where the spindle fibers converge are the centrosomes.