Hope is a Desire for something to happen, while expecting or being confident that it will come true. Hope also implies a certain amount of perseverence, believing that something is possible even when there is some evidence to the contrary. Hope may be directed toward something minor or towards something extremely significant. "False hope" is hoping for something that is extremely unlikely or unrealistic.
Examples include:
The absence of hope is Despair. In some religions, despair is considered to be a sin.
Hope was personified in Greek mythology. When Pandora opened Pandora's Box, she let out all the evils except one-- Hope. Apparently the Greeks considered Hope to be as dangerous as all the world's evils. But without hope to accompany all their troubles, humanity was filled with despair. It was a great relief when Pandora revisited her box and let out hope as well.