Regarding MTB: The tapper allows for a bigger lower bearing while keeping the upper bearing smaller. The lower bearing receives a greater part of the load as most of the time it carries all the weight applied to the headtube and transmits it to the fork. The upper bearing mostly deals with side forces that try to "bend" the fork, i.e. cornering and braking forces.
It also allows for greater contact surface between steerer and crown, which translates into a much more resistant joint. This in turn allows for a longer travel fork that does not require an upper crown.
The final result is that you get a more aggressive front end, without the penalty of adding too much weight and also keeping the bike visually light (double crowns look like motorcycle stuff). These characteristics are preferred for All Mountain and Enduro bikes.
Another benefit of keeping the upper part of the steerer tube small is that you can still use regular stems and stem spacers, star nuts and top caps, which keeps compatibility with a huge range of components already available.