The Euler angle output is designed for applications which need a quick reference to the heading, pitch and roll values, for application where the tilt angles are less than 30 degrees. A typical application would be a digital compass, where the device should be almost parallel to the ground, and the heading output is used. Other applications could be pitch and roll monitoring for remote controlled cars, where it is expected that the device orientation stays the same.
Euler angles are not well suited for describing complete rotations, since when the pitch is 90 degrees, heading is undetermined. The BNO055 automatically changes the reference frame for the Euler angle output, so that no matter in which orientation it is mounted in the device, the output can be used directly. This causes discontinuities when making full rotations.
The BNO055 can be used in application where complete 3D rotations needs to be measured, in which case the recommended sensor output to use is the Quaternion output.