The Euler vector contains the Euler angles. You can read about them here:
https://en.wikipedia.org/wiki/Euler_angles
The Euler angles are referenced to "down" (the gravitational direction) and magnetic north. How these relate to your heading, pitch and roll will depend on how you've oriented the sensor board with respect to the moving platform, as well as whether the platform can only move in one direction with respect to its shape (like an airplane) or multiple directions (like a quadrotor). For an airplane. the heading is always in the direction of the nose. For a quadrotor, the heading can be in almost any direction w.r.t. the platform, which is a problem because the BNO055 has no way of knowing the direction in which it's heading. It can only measure it's orientation relative to gravity and the earth's magnetic field.
The easiest way to visualize how the Euler angles map onto heading, pitch and roll is to print them out while rotating the sensor board in various directions. Having a magnetic compass handy will help. Hold the board level and point it toward magnetic north, then rotate it in the plane while observing the Euler angles. Do the same, but applying "pitch" and "roll" rotations instead of "yaw".
Let us know how it goes.