The availability heuristic is a cognitive bias, a default thought process that can cause us to make errors in judgement.
The original example of the heuristic was an experiment1 in which participants were asked "If a random word is taken from an English text, is it more likely that the word starts with a K, or that K is the third letter?" Most people, in attempting to think which set of words are more common, will more easily recall words which start with K, and respond that these are more likely. (In fact, most texts contain twice as many words in which K is the third letter.)
There are numerous situations in which this heuristic is relevant. For example, we tend to weigh one report by a friend more heavily than an aggregate of thousands of reviews -- even if the review is from an impartial, reliable source such as Consumer Reports.
More sinisterly, we form opinions based on our most easily recalled information. The same person may form a very dim view of welfare if they are given examples of welfare abuse, and very positive view if they are given success stories. This allows media outlets with even comparatively mild biases to polarize populations into angrily opposed groups while reporting nothing but pure facts. This polarization spreads and strengthens as we spend more time with people who share our opinions and information sources, until new or conflicting facts are drowned out in a flood of self-supporting information, happily provided by political parties.
There are no end of examples in which we weigh events too heavily because they are too easily brought to mind; shark attacks, plane crashes, homicide, lottery wins, rabies, and even the end of the world are often believed to be more likely than they really are.
Brevity Quest 2016
1. Tversky, Amos; Kahneman, Daniel (1973). "Availability: A heuristic for judging frequency and probability". Cognitive Psychology 5 (2): 207–232.