Final answer:
Plants achieve indeterminate growth through meristem tissues, specifically apical meristems, which allow for continuous cell division and differentiation resulting in primary growth.
Step-by-step explanation:
Plants are capable of indeterminate growth primarily due to meristem tissues. Meristems are embryonic regions within a plant that possess the unique ability to divide indefinitely. Cells within these regions are undifferentiated and retain the potential to become a variety of cell types. The apical meristems, located at the tips of roots and shoots, are responsible for the plant's primary growth, which includes lengthening of the stem and root system. As a result, meristematic cells are key to the plant's continuous growth and formation of new tissues.