Full width at half maximum (FWHM) is one measure of the width of a hump or valley in the plot of a continuous function. "Maximum" is taken as the maximum amount above (or below, i.e., "maximum depth") the value of the function on either side of the hump or valley, and the value is the width in the "X direction" between points on this hump or valley where the function is half the difference between this maximum (or maximum depth) and the value outside the hump/valley.
The Gaussian function with its bell curve is a function with such a hump. Astrophysics uses the measure as a means to quantify the width of a spectral line, e.g., in formulae that relate the width to other quantities. It is also used to specify passband specifications, sensitivity functions and other similar functions.