Willful ignorance is when people refuse to pay attention to any evidence that goes against their preconceived notions. People who are wilfully ignorant sometimes disregard facts that have been proved if they can hold onto their beliefs better without recognising why their beliefs are wrong. If there are reasonable arguments against their favourite beliefs people who are wilfully ignorant just ignore it. If things happen which don’t meet what a wilfully ignorant person expects it’s just ignored. In other cases, wilfully ignorant people refuse to read, hear or study in any way anything that does not pretend that everything they want to believe is true.
Here's an example: people believe in God because so many other people believe in Him. They are ignoring the gullibility of the human race, because they don't like the fact that their species can be suckered.
Adapted from RationalWiki