Building dimensions begins with a point of zero dimensions. This point can be expanded into one dimension forming a line. The lined can then be expanded into two dimensions so as to form a plane. Finally the plain can be expanded into three dimensions forming a space. This process can continue indefinitely with no theoretical limit to the number of dimensions. In spite of our existence has only three spacial dimensions any number of dimensions is theoretically possible.
In physics dimensions have been classically used to refer to 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 its child M theory uses 11 dimensions. Mathematically there in no limit to the number of possible dimensions from zero to infinite dimensions. In fact Nth dimensional modeling is useful for dealing with any set of properties as if they were physical dimensions.
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.