The realization of the preciousness of their mother tongue was triggered by sudden orders from Berlin. Let's discuss this in detail:

Sudden orders from Berlin:
- The story "The Last Lesson" by Alphonse Daudet is set in a small town in Alsace-Lorraine, which was a disputed territory between France and Germany.
- In the story, the people of the town are caught off guard by the sudden orders from Berlin, which announce that German will be the only language taught in the schools of the territory.
- This news comes as a shock to the people, who have always spoken French and have a deep attachment to their language and culture.
- The suddenness of the orders from Berlin makes the people realize that their mother tongue is precious and that they have taken it for granted.

M. Hamel's words:
- M. Hamel is the teacher who teaches the last French lesson in the school before it is closed down.
- He delivers a passionate speech about the importance of the French language and the need to preserve it.
- His words strike a chord with the people, who realize that they have not been valuing their language enough.
- However, it is not M. Hamel's words alone that make the people realize the preciousness of their mother tongue. It is the sudden orders from Berlin that serve as a wake-up call.

School orders:
- The orders from Berlin also affect the school system in the town.
- The school principal announces that the last French lesson will be taught that day, and that from the next day onwards, only German will be taught.
- This sudden change in the curriculum makes the students and the teacher realize that they have taken their language for granted and have not appreciated it enough.
- The school orders, therefore, play a crucial role in making the people realize the preciousness of their mother tongue.

In conclusion, it is the sudden orders from Berlin that make the people realize the preciousness of their mother tongue. M. Hamel's words and the school orders also contribute to this realization, but it is the suddenness and the magnitude of the orders from Berlin that serve as a wake-up call for the people.