1.
If you fight off something, for example an illness or an unpleasant feeling, you succeed in getting rid of it and in not letting it overcome you.
Unfortunately these drugs are quite toxic and hinder the body’s ability to fight off infection...
All day she had fought off the impulse to telephone Harry.
= resist
PHRASAL VERB : V P n (not pron) , V P n (not pron) , also V n P
2.
If you fight off someone who has attacked you, you fight with them, and succeed in making them go away or stop attacking you.
The woman fought off the attacker.
PHRASAL VERB : V P n (not pron) , also V n P