A senior was a student in their final year of schooling.
As an undergraduate in California, Jonathan Archer was an accomplished athlete in the sport of water polo. During his senior year, he participated in the 2134 North American Water Polo Regionals. Following the victory in the regionals, he and his team went on to participate in the championship round of the tournament that year. (ENT: "Vox Sola")
Ensign Taitt graduated Starfleet Academy in 2369 and wrote her senior honors thesis on solar dynamics. (TNG: "Descent, Part II")
When Julian Bashir was the captain of his racquetball team at Starfleet Medical Academy, they won the Sector Championships in his final year. (DS9: "Rivals")