It's for when you want to block that Obliterating Bludgeon without it getting baited by a Weak Strike. Basically saving your block for the ones that will actually hurt.
It's harder to draw out, because it will only react to higher damage cards. The idea is that it prevents you from taking a big blow, without being wasted on a weak attack. For example, lets say my warrior has a regular block, and my opponent has 3 weak attacks (3 damage) and a strong attack (14 damage). The enemy will use the weak attacks to draw out my regular block, and then he will hit me with his strong attack. So I wind up taking 20 damage. Now let's try the exact same scenario, except with desperate block. If the enemy tries to draw out the block with his weak attacks, the block won't trigger. When he finally attacks with his strong attack, the desperate block (hopefully) triggers, blocking the worst of the damage. So I wind up taking 9 damage. Desperate block also won't be drawn out by elvish insight/maze/heals/dwarven warcry etc, since those don't deal any damage. (edit: didn't see the response above when I posted, basically I'm saying the same thing in more words)
