Well actually I know what gradient is and what that means. My professor once said that gradient is actually a covector in passing. As I know, covector is a linear map that maps vector to a scalar but gradient maps scalar to a vector.
So I guess he meant divergence $ \nabla \cdot $, not gradient $ \nabla $.
By that way, it does make sense considering $ \nabla $ is a vector $ \begin{pmatrix} \frac{\partial}{\partial x^1} & \frac{\partial}{\partial x^2} & \frac{\partial}{\partial x^3} & \cdots & \frac{\partial}{\partial x^n} \end{pmatrix} $ and dot product is defined as $ v^T $ when operating a vector to another vector.
Am I correct or is there something I'm misunderstanding?