Alright. Well right off the bad I will state that this is a class related question, but NOT a homework question. I am currently building my own math library and for that library I need to have an Euler Angle Function for a Vector3, but after a good 2 weeks of searching through any website I would like someone to explain Euler angles from a beginners perspective.
Basically, you have two separate 3-D coordinate systems, both having the same origin, but one is rotated in relation to the other. Euler angles define the component angles of rotation between the two systems.