Misleading Vividness
The act of describing a relatively uncommon, but dramatic event or consequence in great detail and putting emphasis on this event or consequence in such a way that people are left with the impression that the event is much more common than it really is. If used in a negative fashion, it can leave people with an irrational aversion or fear of something, rather than a realistic perspective on potential risks and dangers and their likelihoods. If used in a positive fashion, it can leave them with the impression that potential rewards are far more likely than they really are.
For example, Levi, who has never eaten anything with citrus before, says he wants to try a slice of lemon pie. But his friend Beth tells him not to - "Don't do it! Just the other day Michael bit into an orange and it turned out he was allergic - he swelled up all over, he couldn't breathe, and if we hadn't gotten him to the hospital on time he would have died!" Of course, citrus allergies are relatively rare, so it's unlikely that Levi would have a similar reaction. Beth's graphic description is basically a scare tactic.
Or, Kendra fears the possibility that a stranger might kidnap her six-year-old daughter. She calls a neighborhood meeting, where she reads several stories of young children being snatched off the streets by strangers and describes the horrific things that happened to these children at the hands of their kidnappers. Kendra then says that this is the reason they need to instate a program to watch out for and report anyone walking around the neighborhood who looks "suspicious." Never mind that the odds of children getting snatched off the streets by strangers are extremely low, while the odds that the neighbors will end up calling in false alarms and potentially waste the time of police officers who could be off dealing with actual crime is much higher.
Or, someone running a multi-level marketing scheme might tell new members a series of "inspirational" stories of members who started at the bottom and worked their way up to the top, giving the new members the false impression that they, too can make their way up to the top if they just work hard enough. However, the pyramidal structure of a MLM scheme makes this impossible - only a certain number of people can be at the top and no matter how hard those on lower tiers work, this will not change.
See also Hasty Generalization and Observational Selection.