Push-ups were a form of exercise done in the prone position, whereby the body was repeatedly raised and lowered using only the strength in one's arms.
In 2368, Ensign Reel was doing some push-ups in his quarters when Ensign Ro Laren and Romulan officer Parem ran through him after a transporter accident involving an experimental interphase generator-cloaking device, shifted their bodies out of phase with the rest of the ship. (TNG: "The Next Phase")
In 2375, a confined Tom Paris began to do pushups, counting "One, two, three." When Neelix came to bring him sustenance, he continued with "Ninety eight, ninety nine, one hundred". (VOY: "Thirty Days")