Junior grade was a subordinate rank qualification, existing for both enlisted and officer ranks, that sat one position lower than the unqualified corresponding rank. For example, in Starfleet, a lieutenant junior grade was a subordinate to a full lieutenant.
As the USS Voyager approached the limits of Neelix's regional knowledge of the Delta Quadrant, in 2373, he felt that he needed to find new means of being useful to the crew by showing interest in joining on as one of Tuvok's security officers. After Tuvok neglected to allow Neelix on his security rounds, Neelix assured him that he had completed his study of starship security protocols and that he felt Tuvok should find that he was "fully qualified to serve in the capacity of a Starfleet security officer. Junior grade, of course." (VOY: "Fair Trade")
The same year, when Rom quit his job at Quark's and joined the Bajoran Militia, he was assigned as "one of the station's Diagnostic and Repair Technicians, Junior Grade... night shift." (DS9: "Bar Association", "The Assignment") By 2375, Rom had been promoted from his junior grade position to that of a Maintenance Engineer, First Class. (DS9: "It's Only a Paper Moon")