For questions about the Kodaira dimension of a compact complex manifold $X$, a numerical invariant which takes value in $\{-\infty, 0, 1, \dots, \dim X\}$.
Let $X$ be a compact complex manifold. One way to define the Kodaira dimension of $X$, denoted $\kappa(X)$, is as follows.
The integer $P_d := \dim H^0(X, K_X^{\otimes d})$ is called the $d^{\text{th}}$ plurigenus of $X$. If all the plurigenera of $X$ (for $d > 0$) are zero, then we set $\kappa(X) = -\infty$. Otherwise we set $\kappa(X)$ to be the minimal $k$ such that $P_d = O(d^k)$.
There are other equivalent definitions of $\kappa(X)$, see here.
If $\kappa(X) \neq -\infty$, it turns out that $\kappa(X)$ is an integer between $0$ and $\dim X$; this is not obvious using the above definition. The value $-\infty$ is chosen so that the Kodaira dimension satisfies $\kappa(X\times Y) = \kappa(X) + \kappa(Y)$. If $X$ and $Y$ are birational, then $\kappa(X) = \kappa(Y)$.
If $K_X$ is positive (ample), then $\kappa(X) = \dim X$. A complex manifold with $\kappa(X) = \dim X$ is said to be of general type. Note, not every general type manifold has $K_X$ ample (for example, blowups of $X$ are birational to $X$ but they will not have positive canonical bundle).
