Say you have a polynomial $F(x_1,...,x_n)$ with real or complex coefficient. Then you can consider it as definining a function
where $K$ is either $\Bbb R$ or $\Bbb C$. Simply, the value associated to an $n$-ple $\vec a=(a_1,...,a_n)$ is $F$ evaluated at $\vec a$. In geometric terms, solving the equation
means finding the zero-locus of the function $(*)$ which is some subset $Z_F\subseteq K^n$. The case you are familiar with is that of $n=1$, where $Z_F$ is typically a set of isolated real or complex points.
Studying the geometry of the sets $Z_F$ is the foundational motivation of Algebraic Geometry