Advancement of the cleavage furrow from the outside of the cell inward towards the center of the cell. The cleavage furrow acts as a 'purse string' which draws tight to separate daughter cells during cytokinesis and partition the cytoplasm between the two daughter cells. The furrow ingresses until a cytoplasmic bridge is formed. [ http://www.ncbi.nlm.nih.gov/pubmed/20687468 http://www.ncbi.nlm.nih.gov/pubmed/15811947 ]