In this style of thinking, a person is generally hostile to new information coming in, especially if it conflicts with their existing beliefs. They will find a way to discount, discredit, or rationalize away the conflicting info in order to preserve their existing belief.
We all do it to some degree, but some do it more than others.
Lawyers, not scientists
A good analogy is that people who engage in a lot of motivated reasoning are operating more like lawyers — who are arguing a specific point of view regardless of its veracity — and less like scientists, who are testing a hypothesis in good faith.