There are some cards or effects that tell you to attack a target who is within x spaces of you. For example, the Marshal class card 'I am the Law':

Exhaust this card after a monster within 2 spaces of you resolves an attack that affects you. Perform an attack that targets that monster. Then, you may test . If you pass, suffer 1 , and that monster gains 1 condition of your choice.

Or the Heroic Feat of Andira Runehand:

: Choose 1 hero within 3 spaces of you. Then, perform an attack that targets a monster within 3 spaces of you. The chosen hero recovers equal to twice the amount of the target monster suffers from this attack.

It seems pretty self explanatory to me, but that means that you just, perform the attack, right? So even if you have a melee weapon equipped so you would normally be unable to attack a target 2 or 3 spaces away, you perform the attack, right?

No, when performing an attack that is part of an ability, you still have to follow all steps of an attack. Thus, if there is no valid target in step 1 (Declare Weapon and target) of the attack, it cannot be performed.

Otherwise, e.g. with Advance a Knight would be able to attack anything on the map, as there is no restriction included on the card. Wouldn't that be hilarious?

I understand your point. Does that mean then, that the only reason there's a max. range on Andira's Heroic Feat and the 'I am the Law' card, is so that if you have a ranged weapon you'd still have to be within 3/2 spaces?

Yes.