The character of a representation $\rho:G\to\mathrm{GL}(V)$ is the function $\chi:G\to \mathbb F$ given by $\chi(g)=\mathrm{trace}(\rho(g))$ (where $V$ is a finite-dimensional vector space over the field $\mathbb F$).
The term is also use for homomorphisms $G\to \mathbb F^\times$, which can be seen as a special case of the above definition when the representation is one-dimensional.