What is *physical meaning*?

Let me first ask you a question; what do you think I mean by $$\mathbf{F} = m \mathbf a$$ ?

From a mathematical point of view, the equation expresses the relationship between two vectors.

However, a physicist, when using mathematics to understand nature, makes mapping between physical concepts and mathematical objects. For example for the above case, there is a measurable quantity & a physical concept called force and we are denoting it by a mathematical object, namely a vector, so the mapping is

$$\text{Force (measurable quantity)} \to \vec{F} (\text{mathematical object}).$$

Now, coming back to your question, what do they mean by "physical meaning of a mathematical expression" is the inverse mapping of the above relations, i.e

$$ \vec{F} (\text{mathematical object}) \to \text{Force (measurable quantity)}$$

I understand physical meaning as setting the context.

We can learn a lot about the maths of 2-spin particles, operators, probabilities and expected values for example. But without learning about Zeeman effect and Stern-Gerlach experiment, all the stuff seems coming from nowhere.