What is suppression resist?

"Suppression" and "suppression resist" are the same thing. Suppression is a mechanic that limits the application of debuffs to characters in the game. With exception from some bosses, certain debuffs will only apply to characters that have had their suppression resist sufficiently depleted to different colours. You can tell how much suppression resist you have from the gauge on the bottom left, and enemies with the suppression mechanic will have a suppression gauge under their health bar.

The wiki page describes which stage of suppression applies to different status effects.