Building dimensions starts with a point which has zero dimensions. This can be expanded into one dimension to form a line. The lined can be expanded into two dimensions to form a plane and that plain can be expanded into three dimensions to form a space. This process can be expanded indefinitely with no theoretical limit to the number of dimensions despite the fact that our existence has only three spacial dimensions any number of dimensions is theoretically possible.
In physics dimensions have been classically used with space however Spacial Relativity added time as a dimension. Cosmological Relativity adds cosmic expansion velocity as a dimension. String theory uses from 10 - 26 dimensions and M theory uses 11 dimensions. Mathematically any number of dimensions is possible from zero to infinite dimensions.
Nth Dimensional Modeling is useful for describing more than physical dimensions it can model the distribution of any set of properties expressed as numbers.
While dimensions are primarily used to describe space and time though some physical theories use more than three spacial dimensions specifically string theory. They can also be used to model the distribution of non spacial properties.