Final answer:
Cell theory was most importantly influenced by the invention of the compound microscope, enabling the observation of cells, which led to the fundamental understanding that all living things are composed of cells.
Step-by-step explanation:
The development of cell theory was most importantly influenced by the invention of the compound microscope. Cell theory began with the work of Robert Hooke, who first described cells in 1665 after observing cork with a microscope. Later, scientists such as Theodor Schwann and Matthias Schleiden expanded on these observations, stating that all living things are made up of cells and new cells arise from existing cells. The discovery of microorganisms by Antonie van Leeuwenhoek, using improved microscopy techniques, also contributed significantly to the development of cell theory. The correct answer to the student's question is C) the compound microscope as it enabled scientists to observe and understand the elementary units that make up all living organisms.