Say you have three different buffs, and you use a skill that does 100 damage without any of these buffs.
Buff A = 10% damage bonus
Buff B = 15% damage bonus
Buff C = 20% damage bonus
If the buffs are additive it means they stack like this to increase your damage:
100 * (1 + 0.10 + 0.15 + 0.20) = 145 damage
If the buffs are multiplicative it means they stack like this to increase your damage:
100 * (1 + 0.10) * (1 + 0.15) * (1 + 0.20) = 151.8 damage
If Buff A and Buff B are additive, but Buff C is multiplicative they stack like this to increase your damage:
100 * (1 + 0.10 + 0.15) * (1 + 0.20) = 150 damage
So in summary if a buff is additive, it is first grouped with other like buffs and all added together before they give their damage bonus. A multiplicative buff stands on its own and gives its damage bonus directly on top of everything else. As you can see in this example a buff being multiplicative generally grants it more weight and power in increasing your damage.
I'm sure if you dig a little deeper you can find pre-compiled lists of which buffs fit into the additive category(s) and which ones are multiplicative.