Hume was the Scottish philosopher known for, among other things, the dictum that the wise person apportions his or her belief to the evidence. Carl Sagan later popularize the variation "extraordinary claims require extraordinary evidence." This does not mean that something that is far-fetched and unlikely is impossible, it means that the more unlikely or far-fetched it is the more reluctant we should be to invest our belief in it and the lighter we should hold that belief.
Hume's dictum is made necessary by another of Hume's famous premises--that our emotions make our decisions and our reason supplies the rationale for those decisions. Unfortunately, we tend to believe that we are rational beings. We often overlook the flaws in our reasoning because we think we are rational and we fail to see that our emotions are guiding our decisions or beliefs. Therefore, we can be fooled easily and if we are not careful we end up making poor decisions that are well-protected with a thick layer of flawed logic. Hume asserted this in the 18th century; modern neuroscience confirms it today (see, for example, David Eagleman's book "Incognito: The Secret Lives of the Brain").
Remembering to apportion our belief to the evidence can help protect us from poor decisions in all aspects of our lives. It can help us make better business decisions by using careful analysis to confirm or disconfirm our intuitions. It can help us make better health decisions by look for the evidence of the efficacy of treatments beyond the anecdotes of celebrities or neighbors. The list could go on....
Hume was not dismissive of our intuitions or our emotions, but he understood the need to put them into context and use reason to challenge our assumptions rather than confirm them. He is a philosopher well-worth a little more exploration.
