Cytokinesis differs in plants and animals because unlike animal cells, plant cells have a cell wall that needs to be split up. Mitosis and cytokinesis are not the same thing; mitosis is the division of the components of the nucleus, whereas cytokinesis is the division of the cytoplasm and its constituents.
In animals, a cleavage furrow forms in the middle of the cell that is about to divide. The furrow deepens and constricts the center of the cell until the membrane touches. At this time, the membrane then fuses and totally divides the two daughter cells. The cleavage furrow is controlled by cytoskeletal elements, which pull the plasma membrane inward. These cytoskeletal elements include filamentous actin and myosin and are the same structures responsible for cytokinesis in fungal cells.
Plant cells cannot undergo cytokinesis in the same manner because the cell wall stands in the way: it is rigid and cannot constrict like a plasma membrane. In telophase, the Golgi apparatus, also called the dictyosome in plant cells, produces vesicles that move and line up in the middle of the cell. The vesicles then fuse with one another until a continuous cell plate forms. The vesicles and cell plate that they eventually form contain all the components of a plasma membrane as well as a cell wall.
Prior to cell division, the cell copies its DNA in the nucleus. This creates a duplicate of each genetic instruction needed for a cell to carry out its daily activities. In the first stage of mitosis, the nuclear membrane dissolves, allowing the DNA to be moved to the middle of the cell. Once the DNA lines up in the middle of the cell, the copies are pulled to opposite poles of the cell. Once moved to opposite poles, a nuclear membrane forms around each group, and the cell is ready to proceed to cytokinesis.