I am starting Diablo 2: LoD and I notice that some of the weapons have the bonus like +2 fire damage. What does that mean? Does that mean all my fire skills damage increase by 2?
This is specific to the Weapon only.
The attribute "adds (x-y) Fire damage" only applies to the attacks made with the weapon specifically, and does not apply to any other spell(s) you might have.
This will stack with certain skills that already apply damage to a weapon attack, for example, the Amazon's Exploding Arrow or Immolation Arrow skills. Using a bow that adds fire damage will add an additional amount of fire damage to these skills.
In other cases, like the Sorcerer, using a Staff that deals fire damage only deals that fire damage when you physically attack an enemy with the Staff itself, but will not apply to spells you cast, like Fireball.