Complex sentence: The Ohio State University's intercollegiate sports teams and players are called the "Buckeyes" (after the state tree, the Buckeye), and participate in the NCAA's Division I in all sports and the Big Ten Conference in most sports.
Split into simpler sentences: The Ohio State Buckeyes are the intercollegiate sports teams and players of The Ohio State University, named after the state tree, the Buckeye. The Buckeyes participate in the NCAA's Division I in all sports and the Big Ten Conference in most sports.