It means the density is not varying with the direction. Your mathematical description also indicates it because it is a function of only x, y, z and t; not theta.

ro is scalar, just as temperature or pressure, as opposed to the velocity which is a vector.

In any flow field, the density is a function of space (x,y,z) and time (t).

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It means that density is a scalar quantity.

In physics there are several different quantities that can be classified according to their tensorial order.

The classification sees the following quantities in increasing order:

- Scalars, quantities that can be described simply with a number (mass, density, temperature, pressure...). They are called tensors of zero order. (30 = 1 number)

- Vectors, that can be described by a vector, or a scalar and an oriented direction, or by three scalars which are the vector components (velocty, acceleration, momentum, force....). They are called tensors of the first order. (31 = 3 numbers)

- Tensors (but it should be better to call them as tensors of the second order) that can be described by a tensor, or by three vectors, or a by scalar and two oriented directions, or by nine scalars which are the tensor components (stresses in a fluid or in a solid, strains...; remember what you should have learned in theory of elasticity, where the tensor is generally symmetric so you have six independent components).  They are called tensors of the second order. (32 = 9)

- Then you can go up. For instance, a tensors of the third order are described by 27 scalar components (33 = 27 numbers) and so on. Fourth 81, fifth 243, ...

Strangely enough, the stresses in a fluid which are tensors of the second order, when the fluid does not move (is at rest), reduce to a scalar quantity, the pressure.

@A.K. Keshari - Yes sir now it all makes sense. Thank you for your clear explanation.

@Aurélien Arntz  : Yes, thank you very much.

@Giovanni Maria Carlomagno - Thank you very much sir for spending time on elucidating it very clearly.

it basically mean divergence of density. since density is a scalar quantity. it does not inherently shows the direction. thus different in density between two points in flow filed is expresses as scalar density field or density gradient at point at given instant of time. Thus density can be expressed as vector using scalar density field.