Adverse selection
Adverse selection, anti-selection, or negative selection is a term used in economics, insurance, statistics, and risk management. On the most abstract level, it refers to a market process in which bad results occur due to information asymmetries between buyers and sellers: the "bad" products or customers are more likely to be selected.  A bank that sets one price for all its checking account customers runs the risk of being adversely selected against by its high-balance, low-activity (and hence most profitable) customers.  Two ways to model adverse selection are with signaling games and  screening games.

# Example: Insurance
The term adverse selection was originally used in insurance. It describes a situation where, as a result of private information, the insured are more likely to suffer a loss than the uninsured.
For example, suppose that there are two groups among the population, smokers and non-smokers. An insurer selling life policies can't tell which is which, so they each pay the same premiums. Non-smokers, on average, are more likely to live longer, while smokers, on average, are more likely to die younger. So the life policy is a better buy for the smokers' beneficiaries. The insurance company anticipates or learns that the mortality rate of the combined policy holders exceeds that of the general population, and sets the premiums accordingly. The result is that non-smokers tend to go uninsured.  However, if the non-smokers could buy a policy on terms that are actuarially fair given their characteristics, they would do so. So market failure is involved.
Furthermore, as a result of the higher premiums, not only do some non-smokers who do not want to pay the higher premiums cancel their policies and go uninsured, some smokers who cannot afford the higher premiums cancel their policies and go uninsured.  Since there are fixed costs in running an insurance company, the insurance company must spread the fixed costs across fewer policies.  This results in a reduction of profits or actual losses which forces the insurance company to again raise premiums.
With further rises in premiums, more non-smokers and smokers who cannot afford the higher premiums decide to cancel their coverage and go uninsured.  This means the insurance company has even fewer policies to spread fixed costs across and results in further premium increases.  This vicious cycle continues until the premiums become so high that no non-smoker or smoker can afford the policies or there are too few policies to spread fixed costs across.  At this point, the insurance company goes out of business and no one has insurance.
In the early days of life insurance, adverse selection forced many life insurance companies out of business until the life insurance actuaries learned to compensate for adverse selection and underwriting procedures were improved to minimize adverse selection.
Whether examples of this sort apply in reality is an open question. Smokers may tend to reckless behavior in general, so be relatively disinclined to insure. Or they may be in denial and not want to recognize their enhanced mortality. When the insured are less at risk than the uninsured, this is known as advantageous selection.

# Asymmetric information
Insurance is not as profitable when buyers have better information about their risk than sellers.  Premiums set according to average risk will not be sufficient to cover claims because buyers will be selected for higher risk (buyers carrying less risk are less likely to purchase insurance.) 
In the usual case, a key condition for there to be adverse selection is an asymmetry of information - people buying insurance know whether they are smokers or not, whereas the insurance company doesn't.  If the insurance company knew who smokes and who doesn't, it could set rates differently for each group and there would be no adverse selection.  However, other conditions may produce adverse selection even when there is no asymmetry of information.  For example, some U.S. states require health insurance providers to insure all who apply at the same cost.  In this case, there may not be an actual asymmetry of information: the insurance company may know who is or isn't a smoker, but because the insurer is not allowed to act on that information, there is a "virtual" asymmetry of information.

# The Stock Market
Here, the risk of adverse selection is generally when you do business with people of whom you have no knowledge. This is one of two main sorts of market failure often associated with stocks. (The other is moral hazard.) Adverse selection can be a problem when there is asymmetric information between the seller and the buyer; in particular, a trade will often produce an asymmetric premium for buyer or seller, if one trader has better/more complete information (e.g., about what other traders are doing, the complete trading book for a stock, etc.) than the average. When a buyer has better information than does the seller (or conversely), a trade may occur at a lower (higher) strike price than otherwise. Ideally, trade prices should be set in an environment in which all the traders have complete knowledge of ambient market conditions (or, at least, equal knowledge thereof) .
When there is adverse selection, people who know there is an above-average probability of a certain favorable price move - more than the average investor of the group - will trade, whereas those who know there is a below-average probability of a favorable price move may decide it is too expensive to be worth trading, and hold off trading. In this way, the 'better informed' investors will obtain a trading advantage (i.e., a trading premium) over the others.
One common source of adverse selection in the stock market is insider trading, in which an insider (such as a corporations officers or directors) or a related party trades based on material non-public information obtained during the performance of the insider's duties at the corporation, or otherwise misappropriated.  Many jurisdictions attempt to address this problem by making the practice illegal.