What is the major function of asters of centrosome in a cell?

The answer is formation of spindle fibers.

Asters (Latin word for stars) of centrosomes are microtubules and are formed around centrosomes during mitosis. During prophase, asters and centrosomes move to the opposite sides of the cell. During metaphase, asters extend and connect to the centromere of chromosomes. During anaphase, those microtubules pull the chromatids apart to the centromeres on the opposite sides of the cell.