Quantiles are often considered to be synonymous with quartiles. They are not. Quantiles are the sets that make up an evenly-divided population of values. A quartile is a type of quantile—as is a quintile, a tercile, a decile, and so forth.
To understand how quantiles evenly divide a population of values, consider the following example from Tableau:
In the preceding example, our data points are 2 - 22 by even numbers. Quantiles are set to Quintiles. The Fourth Quintile is calculated thus: 22 * (4/5) = 17.6. The closest value in the population when rounding up is 18. Therefore, 18 is set as the rank that accounts for approximately four-fifths of the values of the total sorted population.
As evidenced in the preceding screenshot, Tableau allows you to view quantiles via right-clicking on an axis and choosing Add Reference Line > Distribution ...