to count, and so to recount: to take a tally of things, or to tell them over one by one as a story
At its root this word means to set things out one at a time. In its plainest use that means counting: tallying stars, days, people, or footsteps until you reach a total. From there the same action carries over into speech. To recount is simply to count out an event detail by detail, laying out what happened in order so a listener can follow it. Hebrew keeps both actions under one word, so counting and storytelling are the same motion aimed at different objects, numbers in one case, events in the other.
The counting sense stays close to arithmetic and measurement: numbering an army, fixing the days of a feast, weighing whether something can even be counted because it is past counting. The recounting sense is where the word does most of its work in the Bible. People recount their dreams, their journeys, their troubles, and above all what God has done. In the Psalms it becomes the verb of public praise and testimony, telling out God's wonders and his name so the next generation will hear them.
The two senses are not far apart. Both lay a sequence open to view. A person who recounts the works of the Lord is, in effect, counting them off, refusing to let a single one go unremembered.