If $x$ is close to (but not equal) to $a$, then $x$ is either
slightly greater or slightly less than $a$. We can explore these
cases separately. The statement $$\lim_{x \to a^+} f(x) = L$$ means
that whenever $x$ is slightly greater than $a$, $f(x)$ is close to
$L$. In this case, we say: "the limit of $f(x)$ as $x$
approaches $a$ from the right is $L$".
$$\lim_{x \to a^-} f(x) = L$$ means that whenever $x$ is slightly
less than $a$, $f(x)$ is close to $L$. In this case, we
say: "the limit of $f(x)$ as $x$ approaches $a$ from the left is $L$".