Is there such thing as a "3-dimensional surface"?
I have seen some authors who use "surface" as an equivalent of "manifolds".
Personally I don't like it when someone refers to an $n$-dimensional manifold ($n\neq2$) as a surface; it is contradictory to intuition. But I wouldn't say it is wrong.
However, in your case, I do think it is wrong to confuse a "3-dimensional surface" with a "2-dimensional surface embedded in $\mathbb R^3$". I'd suggest changing it to "Bring formulas to life by exploring the multiple number of unusual surfaces they can create in three-dimensional space". (The audience probably wouldn't notice a thing.)
Situation 1: the description reads "...3-d surfaces..."
general public: "cool."
mathematician: "bad terminology."
Situation 2: the description reads "...surfaces...in 3-d space"
general public: "cool."
mathematician: "cool and rigorous."
Although as a mathematician I would never use that terminology, your target audience is probably non-mathematicians. Non-mathematicians do understand "three-dimensional surface" better than "embedding of a surface in three dimensions". I think I would leave the text as it is, except replace "multiple number of" by "many".
You‘re correct: surfaces are by definition $2$-dimensional manifolds. Some (not all, cf. the Klein bottle) can be embedded in $\Bbb R^3$, which seems to be what the text is referring to. This enables us to think of an embedded surface as a $3$-dimensional object (the extrinsic view). Nevertheless, the abstract manifold as a topological space with an atlas is $2$-dimensional (the intrinsic view).
Depending on what the exhibit is focusing on this might warrant a more detailed explanation.