While he didn't actually discover *cells* as living units, he was the first to observe and name them. He looked at a thin slice of cork under a microscope and saw small, box-like compartments which he called "cells" because they reminded him of the cells of a monastery.
It was later, in the 1670s, that Anton van Leeuwenhoek observed living cells like bacteria and protozoa using his own microscopes, which were more powerful than Hooke's.
So, while Hooke gets credit for the initial discovery and naming, it was van Leeuwenhoek who truly revealed the world of living cells.