"Pulled to their feet" is not a common way to describe the scene, but it is effective in describing how "moved with emotion and awe" the judges were. The song had a tremendous affect on everyone who heard it. Some people were probably crying with tears of delight and amazement. The judges stood and clapped with delight, as they heard the rendition of the song. There is no way they would sit there and act like this was a normal, run-of-the-mill musical performance.

Yes, I agree with Gena that "pull" is not usually the verb we use with that expression. It is much much much more common to say her song BROUGHT the three judges to their feet. Anyway, as the others said, it just means that the judges gave her a standing ovation.

To be on one's feet means to stand up. The verb "pull" gives an idea of exerting physical strength to move something that's probably hard to be moved. Therefore, when the judges in a contest are pulled to their feet, they are made to stand up, which is a sign of being impressed. On the other hand, when you say you pull yourself to your feet, that often means that you have trouble standing up.

The judges were impressed.