The three main phases of a single cell cycle are: interphase, nuclear division and cytoplasmic division.
With the right techniques, the next stage in the cell cycle, mitosis (M), can be observed using a good light microscope. Early microscopists found it convenient to subdivide the nuclear division of cells into stages that were easily seen under the microscope using colored dyes that stained the chromosomes and some of the other participants.
Nuclear division or karyokinesis is a continuous process, however, and there are no artificial divisions in actively growing cells.
prophase - metaphase - Anaphase
Anaphase starts with the separation of the sister chromatids. The centromeres on each chromosome somehow break, freeing the two halves. Using time-lapse photography, it is possible to watch the chromosome halves move in opposite directions at speeds which can reach 0.2 - 4 micrometers per minute.
This movement is directed and under the control of the spindle fibers and the microtubules. Although it is by no means certain, the most likely mechanism to account for this movement is the continuous polymerization and depolymerization of the microtubules themselves.
If this concept is correct, the spindle microtubules attached to the kinetochores of the sister chromatids, shorten by depolymerization (removal) of protein subunits at their polar ends. This would shorten the microtubule and "pull" on it, tugging the chromosome half towards that pole.
At the same time, the pole-to-pole microtubules (those not attached to the chromosomes) lengthen by adding protein subunits (polymerization). This action pushes the poles further apart (and pulls the chromosome halves further apart).
While this is a possible mechanism to explain how the chromosomes move during anaphase, it is only a hypothesis. No one has definitively shown that microtubules recycle their component parts in this manner, and other hypotheses have been proposed. All models have their flaws, however, and it may yet be that the correct mechanism waits to be discovered.
Anaphase ends when the "daughter chromosomes" reach the opposite poles of the cell, and the very spectacular events of cell-cytoplasm division are initiated.