Rulebook 2.0 Page:42
Melee +X
[spoiler]This creature gains +X attack dice when it makes a melee attack. If the attack makes multiple attacks against the same or different objects, it gains this bonus only for the first attack it can make with this bonus. Does not grant a melee attack if this creature does not have one. Does not affect ranged attacks, damage barriers, or other non-melee attacks.[/spoiler]
FAQ Page:2
Attack Bonuses
[spoiler]Some traits (such as Melee +X) state that “if the attack makes multiple attacks against the same or
different creature, it gains the bonus only for the first attack it makes.” This wording is clarified to say;
“if the creature makes multiple attacks during the same attack action, it gains this bonus only for the first attack it can make with this bonus.” If a creature gains a bonus on one attack but then the bonus
increases for a subsequent attack, on the next attack he may receive the additional bonus gained.[/spoiler]
Example:[spoiler] A creature has a Sweeping attack and Rage +3, and has 2 Rage tokens on him, so he has
Melee +2. On his first attack, he gets +2 attack dice. If the target Counterstrikes and damages the
attacker, the attacker will get another Rage token, so he will now be at Melee +3. On the second attack,
the creature will get +1 attack die.[/spoiler]
Example:[spoiler] A creature with Melee +2 has Battle Fury cast on him, then the creature makes an attack. The free Battle Fury attack counts as a separate action because the Battle Fury spell says to make an free additional quick action attack, so the player would get to apply the Melee +_2 to extra Battle Fury attack as well.[/spoiler]
BTW this has been covered in several other threads but I combined them all here for simplicity.
I hope that helps