Concept of "Rigidity" in mathematics. What is the idea?

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I am reading from the book "Topics in Galois Theory" by Serre.

I came across the word "Rigidity". I am not able to understand this concept.

If I am not wrong, This term was first used by Thompson, He used this concept("Rigidity Method") to show that monster group can be realized as the Galois group over $\mathbb{Q}$.

I don't have any intuition for this concept. I tried reading from the Wikipedia page on "Rigidity", but I got more confused. It says

The above statement does not define a mathematical property. Instead, it describes in what sense the adjective rigid is typically used in mathematics, by mathematicians.

What is the idea ? One more question, What does the adjective "rigid" means in context of Galois theory.