Evolution of the spindle was of central importance to eukaryotic cells. what role is played by the spindle during mitosis?

The role played by the spindle during mitosis is to bring about an orderly distribution of chromosomes to the daughter cell. 
The spindle fibers form a protein structure that divides the genetic material in a cell. They are necessary to equally divide the chromosomes in a parental cell into two daughter cells during both types of nuclear division: in both mitosis and meiosis. During mitosis, the spindle fibers are called the mitotic spindle. 

The spindle fibers are important in the separation of sister chromatids of the chromosomes, at the centromere. This occurs during metaphase to anaphase. The spindle is composed of microtubules. They extend from the poles of the cell and attach to the kinetochore (at the centromere) of the chromosomes and start pulling apart