Mitotic cell division is for the purpose of producing more of the same cells for growth and for repair or to replace old worn out cells. A parent cell's genetic material must first be replicated before it can be distributed to two daughter cells at the conclusion of mitosis.
Before mitotic division occurs, during interphase --specifically the S phase of interphase, the DNA of the organism is replicated. Now, chromosomes are in pairs called sister chromatids.
Centrioles are tiny organelles with the purpose in animal cells to separate and take up a position on opposite sides of the cell. These centrioles are found in the centrosome, an area of the cell where the spindle is organized. The spindle contains fibers that the replicated chromosomes attach to at their centromeres. The spindle fibers help to later pull apart sister chromatids to opposite poles so that later, two new daughter cells will each have a set of chromosomes.
Plant cells lack centrioles, however, they are still able to form a mitotic spindle from the centrosome region of the cell just outside of the nuclear envelope. They go through the stages of mitotic division as do animal cells-prophase, metaphase, anaphase and telophase, followed by cytokinesis.
The end of mitosis is when cytokinesis occurs-- the division of the cytoplasm, which is accomplished in plants by the production of a cell plate, made from vesicles inside the cell. This step occurs during telophase and the materials inside vesicles collect together to form the growing cell plate, which eventually fuses with the cell membrane. Ultimately, it divides the cytoplasm into two daughter cells and later becomes part of the cell wall.
Animals form a cleavage furrow and eventually pinch apart to form two daughter cells.
I hope this clarifies mitosis in plant vs. animal cells! I have attached a diagram of mitosis in plant cells.