Let me help you with your vocabulary. I feel that, if you understand this terminology better, understanding of the rules will follow. Magic is very consistent in its wording, so it helps to understand that.
So I understand the concept of dealing damage in the form of -X/-X to
You do not 'deal damage' in the form of -X/-X. The term 'dealing damage' is reserved for combat (when a creature uses its power-stat) and for 'burn'-spells or abilities that explicitly say 'deal damage'. See, for example, Shock or Spikeshot Goblin.
The card in question is Elven Palisade. But with the example in
my title, what's the point? If I use this enchantment on my opponent
to give a creature of his -3/-0 until end of turn, wouldn't that -3/-0
disappear at the end of my turn and then his creature would be back to
You are right that the effect is not permanent. A -3/-0 will normally not kill a creature, and the ability on Elven Palissade explicitly state that it ends at end of turn.
I notice that you speak of enchanting his creature, but that's not the case here. You have an enchantment in play that has an activated ability (and it's the ability that gives a -3/-0), like Compulsion. This is not an enchantment that is attached to a creature, like for instance Insolence is.
So, when to use this ability? Well, you can activate this ability on his turn. When he attacks with a Trained Armodon, you can sac a forest to give it -3/-0 and avoid getting damaged. If you also block it with, for example, a 4/2 Firewing Phoenix, the Phoenix would kill the Armodon, but stay unharmed himself.
If I was dealing damage and reduced his toughness to 0 or less then I'd understand the significance, it would kill the creature.
Damage does not reduce toughness. -X/-X reduces toughness. Damage stacks until it's equal or greater than a creature's toughness and the creature dies. If a creature is damaged in a turn, but not sufficiently to kill it, the damage wears off.
A special case is dealing too little damage to a creature to kill it, but using another effect to reduce its toughness.