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The fundamental process for the reproduction of plant cells is mitosis. Mitosis is a type of cell division that results in two daughter cells, each genetically identical to the parent cell. This process is essential for growth, development, and repair of tissues in plants. During mitosis, the chromosomes are duplicated and then evenly divided between two new nuclei, ensuring that each new cell has a complete set of genetic information. This process supports asexual reproduction in plants, allowing for the maintenance of genetic stability and facilitating vegetative propagation.

In contrast, meiosis is primarily involved in the production of gametes (sex cells) for sexual reproduction and results in four genetically diverse daughter cells with half the chromosome number of the parent cell. Binary fission is a method of asexual reproduction typically seen in prokaryotic organisms, rather than eukaryotic plant cells. Cell fusion involves the merging of two cells into one, which does not relate to the typical process of cell reproduction in plants. Mitosis is therefore the correct answer as it directly pertains to how plant cells reproduce and maintain their populations.