Asymmetric information is a phrase economists use to describe scenarios when one party has more information than another. Examples are abound: actors know more about the quality of movie they're selling than movie goers; workers know more about how they spend their time than their bosses; borrowers know better than banks how likely they will pay back the loan.
One of the problems that erupt in asymmetric information is adverse selection: when someone chooses something that started off being a bad idea, such as eating a sandwich that the waiter dropped on the floor. But because the customer doesn't have the same information the waiter does, they take a bite. Hence the name--people will select something that isn't in their interest to select.
Many of my students, however, read this as when people choose things that are bad for them, such as driving drunk or smoking. In this latest homework assignment, people would even mention "everyone knows that such and such is bad for you." Then it's not asymmetric information and adverse selection doesn't apply. If you know smoking's bad for you and you still smoke, you are including the health risk as a cost. People might regret this choice later in life, but it's still not adverse selection. Just because you don't agree with their choice doesn't mean its a problem.
The other major issue from asymmetric information appears after the choice is made: moral hazard. When people make an agreement and then one of them figures they can take the other for a ride, that's moral hazard. There's an element of treachery here hence the name: deciding to take advantage of another's trust presents an ethical quandary for the person to overcome. National health care is a classic example. If you give free health care to everyone, you can bet people will visit the doctor a lot more even if it's unnecessary. They'll be less careful, too. More people would smoke.
It's sometimes hard to tell the difference between adverse selection and moral hazard: was this person planning on betraying me or did it just occur to them after I stuck me neck out? But they are real issues that occur in your everyday life and economists have noted several ways people mitigate these problems (especially when hiring and lending). Hopefully, with just five hours before their final, my students understand their application as well.