dimension

of: a coordinate system (e.g. a system of Cartesian coordinates)

is: a 'direction' in which measurements may be made (usually) independently of measurements in other dimensions. In the case of Cartesian coordinates the directions of the -axis, -axis and -axis each represent one of three independent dimensions. The number of dimensions (the dimensionality of the system) is therefore the minimum number of coordinates needed to uniquely identify any point in the region covered by the system of coordinates.

See also dimensional analysis and dimensions for a different meaning.