In economics, information asymmetry refers to the cases in which one participant in a deal has more (or better) information than the other participant.
The information that is not available to all participants is called "hidden information". The participant that knows this information can use it to his own advantage while (or after) negotiating a deal.
In workplace situations, the employer often gives an employee a certain task without knowing exactly how long it might take. For example, fixing a computer could take one day or several days, depending on the skill level of the employee tasked with the repair. In this case, the employee has information his boss doesn't have: If he knows he can fix the problem in one day, he can effectively take the rest of the time off while telling the employer that the repairs will take a few days.
Example: Used cars
When buying a used car, the salesman quite likely has the upper hand: He knows which cars aren't as great as he says, but he will still praise it as the best car ever made. The average car buyer will lack the knowledge (or determination) to check the car for flaws and thus relies on what the salesman says. In this case, hidden information may lead to the buyer making a decision he wouldn't have made if he had known of this information.
When discussing insurances, there can be two cases of information asymmetry.
The first one is that the insurance company does not magically know everything about the person applying for an insurance. For example, a person with a chronic illness will not readily give out this information while applying for a health insurance. This behavior is called adverse selection.
The second case happens after the person got the insurance. The insurance company can't monitor the insured individual, so it won't know if the accident it has to pay for was a genuine accident or the result of sloppiness (caused by the "Who cares? I'm insured, anyway!" mindset). This behavior is called moral hazard.