Used adverbially with 地 to describe slow, deliberate speech or reading — either for emphasis/clarity or to make sure nothing is missed. Compare 一板一眼 (following rules exactly) and 字斟句酌 (weighing each word carefully).
grammar
Structure 一X一Y pairs two near-synonyms (字 "character" + 句 "sentence") to mean "every X, every Y." Same pattern as 一针一线, 一草一木, 一举一动.