I am just going to give an example of what I mean using Skolem's Paradox. I DO NOT want to get into Skolem's Paradox itself or its "resolution."
Skolem's showed that countability is relative in models of first-order formulations of ZFC (assuming ZFC has a model).
For example, take a model 𝔐 of ZFC. Let 𝔐 satisfy the statement "S | S is uncountable." So, there is no bijection B ∈ 𝔐 from S to ℕ. Now, let's just add B to 𝔐 and let 𝔑 be 𝔐 ∪ B. Thus S ∈ 𝔑 is countable.
When there's a mathematical result such as Skolem's Paradox indicating the relativity of countability (at least with first-order formulations of ZFC, this problem does not come up in second-order formulations), we can ask, "Well, is countability actually relative?" Or some derivative questions: "What are the natural numbers, or what does it mean to say there is a bijection between the natural numbers in the real world?" (whatever you take to be "actual" or the "real world")?
More generally, what is the relation of math-objects/results to the real world (however construed)?
Also see the same question asked and answered on the Mathematics site.