The cell cycle, or cell-division cycle, is the series of events that take place in a cell leading to its division and duplication. In cells with a nucleus (eukaryotes), the cell cycle can be divided in two periods: interphase—during which the cell grows, accumulating nutrients needed for mitosis and duplicating its DNA—and the mitosis (M) phase, during which the cell splits itself into two distinct cells, often called "daughter cells" and the final phase, cytokinesis, where the new cell is completely divided.
Since both plants and animals are eukaryotes, both divide in the same way. Plants have chlorplasts and cell walls which animals cells do not and so have to form those as well.