There are several different kinds of thing that could fit that description, though of course as our scientific knowledge advances, matters could change.
There are mathematical theories that apply only approximately to the real world. Euclidean geometry would be an example, since our universe is not perfectly flat. Nevertheless, it works well on a small scale.
There are mathematical accounts of physical theories that have features that don't seem to correspond to any real value for a physical property. For example, in thermodynamics, equations of state sometimes take the form of a cubic equation in the compressibility factor, and such equations may have negative roots, but we have no way to give physical sense to such values.
There are mathematical theories that deploy concepts that don't seem to have any physical analogue at all, as far as we know. Transfinite numbers would fall into this category. We don't know whether the universe is infinite, but even if it is, there is no obvious application of large cardinals. There are other examples where the mathematical concept of infinity yields unreal results. The Banach–Tarski theorem shows that a solid ball can be decomposed into finitely many pieces and then reassembled into two balls of the same size as the original. That wouldn't work in the real world: it holds because the balls consist of an infinite set of points, which are not 'solid' in the physical sense.