I don't have a classical textbook with me, but without here goes:
a) Polarization: every real antenna establishes E and H vectors around it when the energy in the feeder reaches the antenna structure. Conventionally, we think of the E field, because the H field is directly related to it, but 90 degrrees apart in space. Due to the way the current flows on the surface of the conductive elements making up the antenna, most of the E field will be oriented in one vector direction relative to a fixed set of orthogonal co-ordinates, on earth taken to be the horizon. If the direction is parallel to the earth's horizon, conventionally we define this as horizontal polarization, and of course if vertical to the horizon, vertical polarization. If current can be pursuaded by design of the structure to follow a particular curved path, then circular polarization results, and this is right hand or left hand depending on which sense the curved path follows.
b) and c) In the desciption above, I deliberately said "most of the E field", because the flow of current will establish E field in both the hozizontal plane and the vertical plane simultaneously. The ratio of these two vector magnitudes in dB is the cross-polarization level. In a circular polarized antenna with perfect circularity, this will be zero dB, because the E field level that can be measured is the same in the horizontal as well as the vertical plane. If you imagine a fat dipole, however, with the elements horizontal, most of the E field vector will be horizontal. However, some current will flow across the cylinder, around the curved direction, and thus it will set up a vertical E field. Let us assume this level is -15dB compared to the horizontal level. If an ideal horizontally polarized antenna were to be used as a far field source, with no vertical polarization, the level of energy received in the fat dipole is taken as 0dB when they are both in the same plane. If now the perfect antenna is rotated to the vertical, the level received should fall to zero, but will actually fall to -15dB. This is the cross polar discrimination. In my book, it is also the cross-polar isolation, but purists might disagree and argue the point.
Essentially, cross polar discrimination shows the ability of an antenna to separate, in the above example by rotating it, or discriminate, the pure vertical from the pure horizontal polarization of a received signal.
At bottom, life is all about
Sucking in and blowing out.