The tautological line bundle $\mathcal{O}(-1)$of $\mathbb{P}^n$

Question

The tautological line bundle $\mathcal{O}(-1)$ of $\mathbb{P}^n$. Many resources defined $\mathcal{O}(-1)$ as all pairs $(l,z) \in \mathbb{C}^{n+1}$ s.t. $z \in l$. What does it mean?

My guess is that it means that $z$ is in the span of $l$.