Adverse selection is the tendency for the people who expect to use coverage most to be the ones who buy it, at the highest limits, in a market where the seller cannot fully observe how risky each buyer is. The National Association of Insurance Commissioners, the standard-setting body for state insurance regulators, defines it in its glossary as "the social phenomenon whereby persons with a higher than average probability of loss seek greater insurance coverage than those with less risk." Note the framing: NAIC calls it a social phenomenon rather than a behavior, because nobody involved has to be acting in bad faith for it to happen. A person who knows their family history and buys more life insurance because of it is behaving sensibly.
The problem is not confined to insurance. In economics it names any market in which one side knows more about what is being traded than the other, and the better-informed side's choices systematically shift the average quality of what gets sold. The general treatment economists cite is George Akerlof's 1970 paper in the Quarterly Journal of Economics on quality uncertainty in the used car market, which gave the field the shorthand it still uses.