What is the meaning of max() in intro. to algorithms?
Yes, as confirmed by Gokul, $\max(p,q)$ just means the larger one of its two parameters, $p$ and $q$. It can also apply to more parameters such as $\max(p, q, r, s, t)$, where it means the largest of all 5 variables or values.

Its opposite is $\min$, which is used in the same way but means the smaller one of two values or the smallest one of all given values.

You might want to check the list of mathematical abbreviations the next time you get confused by some math abbreviations.