A point has 0 dimensions.
A point gets expanded into a line.
A lined gets expanded into a plane.
A plain gets expanded into a space.
This process can be expanded indefinitely with no theoretical limit. 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.