Who coined the term cell and how?

Hooke had discovered plant cells -- more precisely, what Hooke saw were the cell walls in cork tissue. In fact, it was Hooke who coined the term "cells": the boxlike cells of cork reminded him of the cells of a monastery. Hooke also reported seeing similar structures in wood and in other plants.

Hence, the cell was discovered by Robert Hooke in 1665. He examined (under a coarse, compound microscope) very thin slices of cork and saw a multitude of tiny pores that he remarked looked like the walled compartments of a honeycomb. Because of this association, Hooke called them cells, the name they still bear. However, Hooke did not know their real structure or function. Hooke's description of these cells (which were actually non-living cell walls) was published in Micrographia. His cell observations gave no indication of the nucleus and other organelles found in most living cells.

EXPLANATION: When Hooke viewed a thin cutting of cork he discovered empty spaces contained by walls, and termed them pores, or cells. The term cells stuck and Hooke gained credit for discovering the building blocks of all life. Hooke calculated the number of cells in a cubic inch to be 1,259,712,000, and while he couldn't grasp the full effect of his discovery, he did at least appreciate the sheer number of these cells.

Hooke recorded all his drawings and observations into Micrographia: or Some Physiological Descriptions of Miniature Bodies Made by Magnifying Glasses.