Definition:Quantile/Informal Definition

Definition
Let $X$ be a random variable with cumulative distribution function $F_X$.

Let $p \in \Z_{\ge 1}$ be a strictly positive integer. Let the range of $X$ be divided into exactly $p$ class intervals such that the probability of an instance of $X$ falling into an arbitrary instance of one of these class intervals is equal to $\dfrac 1 p$.

That is, the class intervals are designed so as to have the same number of elements in them.

Then the class boundaries are known as the quantiles of $X$.