Relative Standing vs Percentile

A raw number says little until you know what it is being compared with, and relative standing supplies that comparison. Percentiles give position by rank, while z-scores give position in standard deviations using $z = \frac{x - \bar{x}}{s}$, where $\bar{x}$ (x-bar) is the mean and $s$ is the standard deviation. A score of 88 on a test with mean 80 and standard deviation 4 has $z = (88 - 80)/4 = 2$, so it sits 2 standard deviations above the mean, near the 98th percentile if the scores are roughly normal. The same raw score can rank very differently in two classes whose means and spreads differ.

The kth percentile is the value at or below which about $k$ percent of the observations lie. For example, if your test score is at the 85th percentile, roughly 85 percent of test-takers scored at or below you. Quartiles are percentiles too: the first quartile is the 25th percentile and the median is the 50th. Percentiles let you compare a single value to a whole distribution without knowing its shape.