What's the meaning of "what it means for {something} to be {something}"?

There is this context:

"We are not only talking about change. Rather, we are discussing what it means for an object to be that object. What does it mean for a certain institution to be that institution? When we say that a certain object changes, we mean that it had a certain property beforehand and after the change it does not."

(The Outer Limits of Reason: What Science, Mathematics, and Logic Cannot Tell Us)

I don't get this part:

"Rather, we are discussing what it means for an object to be that object. What does it mean for a certain institution to be that institution?"

I should note that this is a philosophical book and is talking about personal identity.

Answer

“what it means for {something} to be {something}”

Explained shortly: We have something. What is special / specific about that something which makes it different from something else, even if they are similar?

Example-1: We have a carrot. What makes the carrot to be a carrot? What is specific to the carrot that makes it different from parsley?

When we say that a certain object changes, we mean that it had a certain property beforehand and after the change it does not.

Example-1 (Cont'd): We have an orange carrot. Even if we look at a purple carrot, it is still a carrot, it still cannot be confused with parsley or celery. So, in spite of changing the color, the nature of the carrot did not change.

So, the nature of the object (the carrot) is not changed, even if some change occurred (the color).

The property beforehand: color orange.
The property after: color purple.

NOTE: We assume (most likely, against scientific knowledge) that an orange carrot can become purple. Artificially it may be possible, by feeding it some pigmented water.

Example-2: A child (human) transforms into an adult (human), but the nature (human) does not change.

(image taken from Burpee catalog on Mar. 19, 2019)