Ageing (British English) or aging (American English) is the process of becoming older. In the narrow sense, the term refers to biological ageing of human beings, animals and other organisms.In the broader sense, ageing can refer to single cells within an organism (cellular senescence) or to the population of a species (population ageing). Accumulative-waste theory: The biological theory of ageing that points to a buildup in cells of waste products that presumably interfere with metabolism. 2  Evidence supporting this theory is the presence of a waste product called lipofuscin leading to age pigment.