What does HAMP mean, computer fan context?

It stands for High Amperage Fan. There should be a header (pins) on the board for you to plug in multiple fans or fans that are higher current. H-Amp fans usually have better cooling.

The manual setting for that board would allow you to set measure points and min/max temperatures, etc.

Search "High AMP" at this Asus page: https://www.asus.com/us/Motherboards/ROG-RAMPAGE-V-EDITION-10/

It is High AMPerage header connection for a fan on Asus motherboards, which can provide up to 3 A for powerful fans.