Easy Definition of Availability Bias: Don't think you'll win an argument with one prominent example. If you try that you might be showing Availability Bias.
Geeky Definition of Availability Bias: Availability Bias is the tendency to let an example that comes to mind easily affect decision-making or reasoning. When making decisions or reasoning, the Availability Bias occurs when a story you can readily recall plays too big a role in how you reach your conclusion.
An Example of Availability Bias
She's been smoking since she was nineDeciding to continue smoking because you know a smoker who lived to be 100 would be a good example of Availability Bias. In this scenario, the story you can recall plays too big a role in your decision to continue smoking. A review of medical statistics on smokers' health ought to be a far weightier factor in the decision process.
Sufferers of the Availability Bias (and that's most of us) will think that the likelihood of an event is proportional to the ease with which they can recall an example of it happening.
Another Example of Availability Bias
Persuading a flight phobic to get on a planeThe root of flight phobics' phobias is likely to be how memorable air crashes are. Often, people who are scared of flying cannot control their Availability Bias. As they're able to recall the crash scenes they've seen on films and the news easily, the idea of crashing becomes a far weightier factor in their decision whether to fly.
This is why telling them that at least 66% of passengers survive plane crashes can be a far more comforting statistic for them than saying only 0.0001% of flights crash (actually, instead of "crash," try saying "incidents classified as a crash" to reinforce the 66% survivability).
A Practical Application for Availability Bias
Win an argument using their evidenceWhen someone cites a well-known story as an example to support their argument, you can easily and quickly undermine their position by claiming they are showing Availability Bias.
Let's imagine you're contesting someone's claim about great white sharks being prevalent around the United Kingdom.
Them: "Well, what about the great white shark that beached itself in Newquay in the 1960s?"
You: "That's Availability Bias. You can't put too much weight on one well-known story."
Availability Bias is closely related to Attentional Bias. This means you can usually throw Attentional Bias at them too by telling them they're not considering all the times when the event they've highlighted didn't happen (e.g., when smokers didn't live to be 100, when great white sharks were not seen). Just by being aware of these two biases, you can accuse them of two biases using their evidence (and all this without expending too many calories on thinking). Even better, your statistics-flavored "attack" will be difficult for your opponent to counter.
Summary of Availability Bias: If you think someone is putting too much weight on a story because it comes to mind easily, tell them they are affected by Availability Bias.