what is cross polarization

Suppose u have a vertical polarize antenna. The response of ur reference antenna to an horizontal polarize antenna is refereed to as cross polarization

Couple these terms in your thinking Matched-Pol and Cross-pol. Cross-pol radiation is orthogonal to the matched polarization.

The example cited above is correct. Now consider a RHCP radiator, the cross-pol response is LHCP. If you have slant-45 deg to the right, the cross-pol response is slant-45 deg to the left.

Hopefully that makes sense.

This reference gives you a discussion in grand detail:

Warren L. Stutzman, Polarization in Electromagnetic Systems, Artech House, Inc., 1993.

Here is a very good article a about polarization measurement from Hickman book. Look for the file in the post
https://www.edaboard.com/viewtopic.php?p=427532#427532
Polarization measurement
T. G. Hickman, J. S. Hollis and L. Clayton, Jr.

Imagine you are fishing on a lake. The sun is beating down and glaring off the water. You take out your polarizing sunglasses and rotate them while looking at the glare, and at one rotation the glare goes away, and another rotation 90 degrees from the first, the glare is strongest.

What you are seeing is a polarized electromagnetic wave (sunlight) and you are filtering out or letting in that one polarization.

You can rotate some antennas, like a dipole, the same way, and capture a lot of the transmitted RF signal (when the antennas are in-polarization), or capture very little of the transmitted RF signal (when the antennas are cross-polarized).