In his book Vibrational Medicine, Richard Gerber uses the term Higher Dimensional to describe subtle-energy systems which vibrate at speeds faster than light, i.e., non-physical energies. (Source: R. Gerber, Vibrational Medicine, Glossary).
The term is also used in a more generic meaning as referring to any - typically physical - dimensions beyond our 3D spacetime. String Theory, e.g., uses a model of spacetime that has 10 or 11 (or in one version even 26) physical dimensions. All the dimensions beyond the 3D spacetime we experience are higher dimensional. In this sense, it is a synonym for terms like interdimensional, extradimensional, intradimensional, and other dimensional.
To add to the confusion, several authors use the term higher dimensional where they actually mean from higher densities of consciousness, that typically are more subtle in nature than our material 3D realm.