What does 80% or 60% of Fresnel zone mean?
It's the cross sectional area of obstructions in the Fresnel Zone that matters.

Most of the signal power travels in the first FZ. If you obstruct 20 to 40% of that, the remaining 80 to 60% amounts to about 1 to 2dB loss. For 'most' link budgets, that would be acceptable. Rules of thumb is about what 'most' people would find acceptable.

The nice thing about wikipedia is that they tend to give references for claims made in the text. In the text where they mention 40% or 20% obstruction, they refer to this citation [1]


  Coleman, Westcott, David, David (2012). Certified Wireless Network Administrator Official Study Guide. 111 River St. Hoboken, NJ 07030: John Wiley &amp; Sons, Inc. p. 126. ISBN 978-1-118-26295-5.


where you can find more detail on it.