You can see why this diagram is called the Hubble tuning fork. Hubble believed that galaxies started at the left end of the diagram and evolved to the right. He called the elliptical galaxies "early galaxies" and the spirals "late galaxies."
We now know that he was wrong: galaxies do not move down the forks of the diagram as they evolve. We know this because spiral galaxies rotate quickly (on an astronomical scale), while elliptical galaxies do not. There is no way that an elliptical galaxy could spontaneously begin rotating, so there is no way an elliptical galaxy could turn into a spiral galaxy.
Although Hubble was wrong about his theory of galaxy evolution, his diagram provides a useful way to classify galaxies. In fact, astronomers today still use his terminology: elliptical galaxies are still referred to as "early galaxies" and spirals as "late galaxies."