in the "A Primer on Mapping Class Groups by Benson Farb and Dan Margalit" we define intersection number as follow :
Let $\alpha$ and $\beta$ be a pair of transverse, oriented, simple closed curves in $S$. Recall that the algebraic intersection number $\hat{i}(\alpha, \beta)$ is defined as the sum of the indices of the intersection points of $\alpha$ and $\beta$, where an intersection point is of index $+1$ when the orientation of the intersection agrees with the orientation of $S$ and is $-1$ otherwise. Recall that $\hat{i}(\alpha, \beta)$ depends only on the homology classes of $\alpha$ and $\beta$. In particular, it makes sense to write $\hat{i}(a, b)$ for $a$ and $b$, the free homotopy classes (or homology classes) of closed curves $\alpha$ and $\beta$.
what is mean of transverse ? when two curves are transverse ?