The ignorance of the man in "To Build a Fire" is our ignorance: the ignorance of the human race with respect to nature. London's use of dramatic irony gives us an omniscient perspective on things, allowing us to take a step back and see not just the man's delusions with regards to his immediate surroundings, but also the lack of awareness and understanding we often show towards our own natural environment.
Right from the start we're painfully aware of the man's delusions. When the "old-timer" warns him against travelling alone, the man scoffs at him for being "womanish." Even without knowing what subsequently happens, we sense the danger. Scientific evidence is also blithely ignored by the man. He thinks that 50 degrees below zero is cold and uncomfortable, but that's all; he thinks he can get through it with thick socks, ear muffs, and warm moccasins. Though the man chooses to remain ignorant, this is still an example of situational irony, as we know something he doesn't know or care to know.
Dramatic irony creates suspense in the story because we sense that something unpleasant is going to happen to the man, but we don't know quite what. Maybe he'll go through several terrifying ordeals before emerging victorious in the end—cold, frostbitten and hungry, but much wiser, and crucially, still alive. Even if we've never read the story, and even if we don't know the ending, we know something the man doesn't—the old-timer was right all along. Unfortunately for the man, he only comes to realize this when it's far too late.