early 15., progresse, "a going on, action of walking forward," from Old French progres (Modern French progrès) and directly from Latin progressus "a going forward, an advance," noun of action from past-participle stem of progredi "go forward," from pro "forward" (see pro-) + gradi "to step, walk," from gradus "a step" (from PIE root *ghredh- "to walk, go").
In early use in English especially "a state journey by royalty." Meaning Figurative sense of "growth, development, advancement to higher stages" is by c. 1600, perhaps 15c. (the senses are not easy to distinguish).
To be in progress "underway" is attested by 1849 and preserves the older sense of "a course," whether good or bad (as in Hogarth's "Rake's Progress"); earlier it meant "in sequence" (as the volumes of a book), mid-15c. Progress report is attested by 1865.
1590s in the etymological sense of "move forward or onward in space;" c. 1600 in the figurative sense of "move toward something better, advance on the line of development or improvement;" from progress (n.).
OED says the verb was obsolete in English 18c. but was reformed or retained in America and subsequently long regarded in Britain as an Americanism. Of work, etc., "continue onward in a course," by 1875. Related: Progressed; progressing.