Well, The Lion King had a lot of good talent going into it and had people making good use of the somewhat limited budget it had. It's really telling that this film's animation looks better than Pocahontas's, even though that had more money going into it. Anyway. It's popular because:
1. Disney advertised the hell out of it.
2. Disney was (and is still) very popular, at the height of the Renaissance of the 90s.
3. Brisk writing, compelling characters, excellent animation, a well-paced story, a good story, great music, and great atmosphere.
The ingrediants just kinda came together perfectly for this to be an instant classic.