General term for a person who competes in sports; neutral and widely understood.
彼はプロの運動選手です。
He is a professional athlete.
運動選手は毎日厳しいトレーニングをする。
Athletes do rigorous training every day.
運動選手 explicitly means an athlete, while 選手 is the shorter, far more common everyday term covering any player from pros to school teams.
運動選手 is a slightly formal, native Japanese term for a sportsperson, whereas アスリート is a borrowed English word with a more modern, glamorous connotation.
Compound of 運動 (うんどう, 'exercise, motion') and 選手 (せんしゅ, 'player, competitor').