Mathematically speaking, is a "signal" a function or the set of outputs from a function
A signal is a physical quantity (e.g. voltage) carrying information, or a set of values (e.g. samples in discrete case) of the given function for different values of the underlying independent variable. 

In the diagram above $\epsilon(t)$ is a mathematical modeling (i.e. function) that characterizes the set of inputs (i.e. scalers) going into the controller. 

Strictly speaking, a signal is the "observed" (measurable) physical quantity while a function is a mathematical model (abstract representation) describing the relationship between the involved variables.