What is the intuition behind quantile in scipy.stats.beta.ppf? I'm trying to use scipy.stats.beta.ppf(q, a, b), where q is referred to as quantile. I understand how beta works and its details, but I'm not able to make sense of q here (It is also called as lower tail probability). I mean, why lower tail probability here in this function ? What benefit does lower tail probability gives us here ? What exactly does q (the lower tail probability) in the above function mean and how to understand the same and its intuition ?

Let $X$ be a (univariate) random variable, beta-distributed in your case.
A quantile $q$ is defined as the value $x$ such that $P(X\le x)=q$. That is, quantile $0.5$ is the value $x$ such that half of the density is $x$ or lower. For any symmetric beta distribution, quantile $0.5$ happens to be $0.5$. For asymmetric beta distributions, quantile $0.5$ could be much higher or lower, depending on the specifics of t he density.
If you understand percentiles, quantiles are extremely similar, just expressed on $[0,1]$ rather than $[0,100]$.
