Electrostatic potentials, $V$, and gravitational potentials, $\Phi$, are examples of scalar fields. A scalar field is any scalar-valued physical quantity (i.e. a number with units attached) at every point in space. It may be useful to think of temperature in a room $T$ as your ideal of a scalar field.

The symbol $\rr$ represents the position vector which points from an arbitrary fixed origin (that you get to pick once and for all at the beginning of any problem and must use consistently thereafter) to a given point in space. We often write the symbol that represents a scalar field with “$(\rr)$” after it to indicate that the scalar field may vary from point to point in space, e.g. $V(\rr)$, $\Phi(\rr)$, or $T(\rr)$. In spite of the fact that the symbol $\rr$ has a vector sign over it, the name of the scalar field (e.g. $V$, $\Phi$, or $T$) does not, since the value of the scalar field at each point is a number, not a vector.