The electrostatic potentials, $V$, and the gravitational potential, $\Phi$, 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 the 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. For example, we write $V(\rr)$, $\Phi(\rr)$, or $T(\rr)$ for the electrostatic potential, the gravitational potential, or the temperature, respectively. Even though the symbol $\rr$ contains a vector sign, 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.