The reason was that his patron Prince Nikolaus of Esterházy took up the baryton and wanted lots of music to play. Haydn leapt into the task immediately after having received a complaining letter in which he is "urgently enjoined to apply himself to compositions more diligently than heretofore," especially works for the baryton.
The baryton was an odd sort of instrument, basically a viola da gamba with sympathetic resonating strings. A copy of the prince's instrument is pictured above. The vast majority of the trios were for the ensemble of viola, baryton and cello, all lower register instruments. Haydn also crosses the parts so you aren't quite sure who is doing what. But, as usual, he writes a lot of lovely music, if of a slightly somber cast. Some of the best movements are slow. Here is Trio No. 14 in D played by the Esterházy Ensemble. The movements are Adagio, Allegro, Minuet:
And I apologize for inflicting on you either a new composition or, shudder, even worse, a new genre!