A very short span of time, literally 'a sun (寸) second'. Extremely rare and literary; not used in everyday speech. Modern equivalents include 一瞬 (いっしゅん) or 瞬間 (しゅんかん).
寸秒を争う事態だ。
It's a situation where every moment counts.
Compound of 寸 (すん, a traditional unit of length about 3.03 cm, often used metaphorically for a very small amount) and 秒 (びょう, second). The combination suggests an extremely brief interval, but the exact historical derivation is uncertain.