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Although it’s based upon the height of the lowercase “x” glyph in a typeface, x-height also considers the height of the lowercase characters that have no ascenders nor descenders; this indicates how tall or short the type appears in typical lowercase or mixed-case settings.
Generally, conversations around x-height are about legibility, because a typeface with a small x-height has longer ascenders and descenders.
The x-height itself is measured from the type’s baseline to the height of lowercase glyphs, not including any ascender or overshoot. Because many glyphs have overshoots or rounded tops, the top of flat glyphs such as x, y, and z are easier to measure—hence “x-height.”