So I was battling battling the water Elite Four, and Asher (Delphox) got hit by Gyarados' Waterfall, but he stayed at 1 HP and the little words said "Asher held on to show it's best side toward CLASSIFIED NAME. What does that mean?
If your Pokemon has high affection in Pokemon-Amie (the heart things) then sometimes, if there would be a hit that would knock out your Pokemon, it would survive with one HP and have that message show up. Lucky you.
If your Pokemon has every high affection in Pokemon-Amie, there's a rare chance they will survive a what would be a one hit knockout (OHKO) Source: Serebii (I'm on my kindle, so I can't pos t links\Experience