Exterminate can be really mean if furia has the stun duration boosted almost killing non frontline champions with the damage dealt during the stun alone. getting Resilience will shorten this stun Giving you the chance to excape.
Furia is a high damage healer mostly for her pyre strike. this can seal kills and stop flankers in their tracks but it takes a long time to spawn just attacking her can bait her to use it and juke her out and seal the kill.
Fuiria's solar blessing stops on allies this means that you want to make sure your not too close because it still does damage avoid the beam and focus cauterize on the target or kill furis to keep her from using it again.