A set of lines is said to be in general position if no $3$ of them meet in the same point. What is the reason of this definition? In $\mathbb{P}^2$, i can understand that two generic lines meet in a single point. But, for example, in $\mathbb{P}^n$ with $n \geq 3$, aren't two generic lines, intuitevely, supposed to not intersect at all? (I imagine two generic lines as being skew). But, according to this definition, two intersecting lines in $\mathbb{P}^n$ with $n \geq 2$ would still be in general position.
Is there a better way to understand the notion of general position, maybe using Zariski topology?