霎 originally meant 'a brief shower of rain' — a short, sudden burst. From there it generalized into the 'split second' sense. Compare with 刹那 (chànà, from Sanskrit kṣaṇa, 'instant') and 转眼 (zhuǎnyǎn, 'in the time it takes to turn one's eye').
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Slightly literary; in casual speech 一下子 (yíxiàzi) or 突然 (tūrán) is more common. 霎时间 is favored in narrative writing where you want a touch of drama.
