What technological advancement was necessary before scientists could begin to observe cells?

The correct answer is the invention of the microscope.  

Cells are the finest and the smallest functional and structural unit of a living species. They comprise of cytoplasm and nucleus, which are enveloped in a membrane. The cells are not visible to the naked eye and hence a microscope was required to witness them. Robert Hooke was the first of the scientist to witness them under the microscope.