It depends on the point of space-time, but at each point of space-time it is just a scalar value, unlike a vector for a vector field. Moreover in physics we cla

It depends on the point of space-time, but at each point of space-time it is just a scalar value, unlike a vector for a vector field. Moreover in physics we classify fields by their Lorentz transformation properties/representation. So when we say scalar field we actually mean that is transforms in the "(0,0) representation" of the Lorentz group (although then it's not yet specified whether one means scalar or pseudoscalar). If it were the same at all space time points it would be a constant, and rather boring (more like a cosmological constant).