People tend to confuse skepticism and denialism. Remember that skepticism means, "Following the evidence wherever it leads," for the purposes of our discussion. Denialism, therefore, means, "Refusing to believe a claim no matter how much evidence supports it."
Let's look at the Holocaust. You've heard the stories about millions of Jews being murdered by the Nazi regime but is it true? Could 20th century human beings really have committed such an atrocity? You don't want to believe that a white, Christian society could have really done such a thing so you investigate.
You read everything you can find and the accounts give you graphic detail about the murders, the methods, the locations, and the graves.
You interview survivors and their families. You hear their stories firsthand and see the numbers tattooed on their arms. You're still not sure.
You see the photographs and videos of the bodies piled into mass graves. You're still not sure.
You go to the museums and the former concentration camps. You see the relics for yourself.
Then you walk away saying, "It's all made up. It didn't really happen (or it didn't happen the way history says it did). You've fallen into the realm of denial because you have ignored or dismissed all the evidence in favor of your preferred conclusion.
Holocaust denial is not the only kind of denialism prevalent in our society. AIDS deniers (like Bryan Fischer of the AFA) claim that HIV does not cause AIDS despite the mountains of evidence we have demonstrating that it does. Vaccine deniers claim that vaccines cause autism or that vaccines are all harmful despite evidence to the contrary. The problem is not so much that these people are wrong - it's that they will cling to their erroneous beliefs no matter how much evidence is presented to them. The more you show them they are wrong, the more they dig in. They simply cannot be wrong.
Recently, we've seen a very good example of the difference between skepticism and denial in the climate change community. We know that there are climate change deniers who, in the face of all contradictory evidence, insist that the earth is not warming. They could be standing in front of a boiling ocean and they still wouldn't admit that something is going on. They are deniers.
But Richard Muller is not a denier - he's a skeptic. He didn't think there was anything to this climate change notion. He thought the previous studies might be faulty so he did his own independent examination of the evidence. At the end of the day, he discovered that the other research teams were right and climate change really is happening. He changed his position based on the new evidence. That is skepticism and it's very different from denial.
What about religious denialism? I'm sure you've heard people say, "I don't care how much evidence you have, I have faith and I'll never stop believing in God." You've probably also heard people say, "Evolution isn't true because the Bible says God created the world in 7 days." These people will deny any fact in order to cling to their beliefs. They are not willing to change their minds. Period.
Denialism can be very dangerous for the individual and for society. By pretending that problems don't exist, it's easy to forget the hard-won lessons of the past. By pretending a horrible disease is behavior-based rather than rooted in germ theory, it's easy to demonize and persecute those who have the disease. By pretending that all vaccines are dangerous and do no good, millions of people become at risk for diseases that long should have been eradicated.
Let me be clear here: there is nothing wrong with questioning established claims or challenging the evidence that we accept regarding them. That's actually an important part of the scientific process. But once the jury is out and all your questions have been answered, you have a duty to change your mind and accept the evidence. If you persist in disbelief and continue to throw mud seeing what will stick, you've become a denier.
Ultimately, it comes down to whether you want to live a life of truth or falsehoods. Denial is for those who want to cling to falsehoods no matter what. It's easy to fall into, especially when the belief you hold is very important to you. No one is immune so we must always be vigilant and continue to go wherever the evidence leads.