In 1870 It was annexed to the rest of Italy, the Pope lost his temporal power and it was made into the capital of the newly unified state. That meant moving all the administration and building a lot of new areas. That is on top of industrialization and a more general population boom.

The point is more how small it was just before that: a population of around 50k and much of the Roman ruins in the center used as a pasture.

Industrialization.