A quaternion in general is an extension of a complex number into 4 dimensions. So no, they are not just x, y, and z, and an angle, but they're close. More below...
Quaternions can be used to represent rotation, so they're useful for graphics:
Unit quaternions provide a convenient
mathematical notation for representing
orientations and rotations of objects
in three dimensions. Compared to Euler
angles they are simpler to compose and
avoid the problem of gimbal lock.
Compared to rotation matrices they are
more numerically stable and may be
more efficient.
So what are the 4 components and how do they relate to the rotation?
The [unit quaternion] point (w,x,y,z) represents a
rotation around the axis directed by
the vector (x,y,z) by an angle alpha
= 2 cos-1 w = 2 sin-1 sqrt(x2+y2+z2).
So back to your question,
Meaning if you have X=0, Z=0 and Y=1
the object will face upwards?
No... the object will rotate around this <0,1,0>
vector, i.e. it will rotate around the y axis, turning counterclockwise as seen from above, if your graphics system uses right-hand rotation. (And if we plug in w = sqrt(1 - (0 + 1 + 0)), your unit quaternion is (0,0,1,0), and it will rotate by angle 2 cos-10, = 2 * 90 degrees = 180 degrees or 2 pi radians.)
And if you have Y=0, Z=0 and X=1 the object will face to the right?
This will rotate around the vector <1,0,0>
, the x axis, so it will rotate counterclockwise as seen from the positive x direction (e.g. right). So the top would turn forward (180 degrees, so it would rotate until it faced downward).