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Slashing damage is the third physical damage type, and it refers to cutting attacks of the kind delivered by a sword or an axe, or by a monster’s claws.
While few creatures have vulnerabilities, there are many that have resistances to multiple damage types, and then one damage type missing. So for instance, treants are not vulnerable to slashing damage, but they _are_ resistant to bludgeoning and piercing. In a sense, they have a sort of pseudo-vulnerability to slashing by way of being resistant to other weapons. It certainly makes sense that a tree person would find an axe more concerning than a rapier.
One type of monster you want to watch out for if you’re dealing slashing damage is oozes. There are a few different types of jelly and slime that split in half when they’re dealt sufficient slashing damage.