A limited understanding of dimensional theory in a question like this is like having a hammer with no handle.

2d planes can be described as existing within 3d space, and for this reason they are extremely useful in physics, both for conceptualization and calculation. (for example, height and length trajectory calculations).

3-D, in reality, is a dimensional shorthand similar to 2-d shorthand. We know that time is considered to be a dimension. When you intend to organize an event, for example meeting someone in their office, you need to know the street address of the building (2d: 11th and Madison, for example), then you need to know the floor number ( the third dimension) and finally you need to know what time to meet him. (the fourth dimension,)

String theory suggests that the 5th thru 11th dimensions exist in tiny finite closed loops in the shape of "calabi-yau" spaces. Since these spaces are both self-enclosed and so extremely tiny (smaller than the planck length, or the smallest unit of measurement in modern science), these dimensions are for most purposes irrelevant, so we use the 4-dimensional model.