The Euler angles are three angles that describe the orientation of a rigid body. There are twelve different conventions when talking about Euler angles. In V-REP, Euler angles alpha, beta and gamma (or (a,b,g)) describe a rotation composed by three elemental rotations:
[Euler angles convention in V-REP)]
where Rx, Ry and Rz represent elemental rotations about axes x, y and z respectively, of the absolute reference frame.
For a rigid body, or scene object, you can obtain the same transformation if you rotate it in following order about its own reference frame: rotation of alpha about own X, followed by a rotation of beta about own Y, followed by a rotation of gamma about own Z.