When Star Trek: Voyager's living doctor died at the beginning of the pilot episode, the ship had to activate a previously unseen feature of all starships. It was the holographic emergency doctor, who was meant to be a temporary presence until the ship could return to Starfleet. With Voyager light years away from known space, the hologram doctor became a permanent presence onboard the ship.
Since we learned that every ship has a holographic doctor, it would only be natural that he would appear on other Trek projects, even though his main ship was stranded on the other side of the galaxy. Paramount took advantage of this in Star Trek: First Contact, which featured a humorous scene where the holographic doctor is activated to distract a Borg attack. It would be a rare instance in which a Trek character would cross over from television into film.
