Euler angles are what most people think of when the picture 3d space. Each value represents the rotation in degrees (it could technically be in any units) around one of the 3 axises in 3d space. Also note that Euler angles are the ones displayed in the inspector assuming you are not in debug mode. Most of the time you will want to create angles using eulers because they are conceptually the easier to understand. The flaw is that Euler angles have a problem known as the gimbal lock that prevents certain rotations when two axises align. The solution: quaternions.
Honestly, I don't know what quaternions are. The are a 4 component value represented as
There are almost 0 instances when you will want to manipulate the values in a quaternion individually, so you really don't need to know how they work unless you plan on creating your own engine, Unity abstractifies most of it away. Instead, use the methods Unity provides and know that the
I would recommend learning Euler Angles, they are easy to understand, and very valuable. You can learn how Quaternions work if you want, but you can do almost everything you need to without directly manipulating them. Instead use functions such as