Can you explain specific market failures (asymmetric information and externalities)?

A market fails when it results in an inefficient allocation of resources. In the case of externalities, the market fails to take into account these costs and benefits which results in an over or under production of goods respectively. An example is education which generates a positive externality. The market will have a lower output of education that is desirable and thus a market failure exists.

In the case of asymmetric information, the market can result in transactions that aren't mutually beneficial and thus shouldn't have taken place. These types of transactions don't add value, they just transfer wealth. An example is insurance of someone who knows they are sick but the firm doesn't. When the person gets insurance, the firms essentially gives money to the person for free as they mispriced him.