In general, information asymmetry means that one party has relevant information which is not known to the other party of a transaction. In Health Insurance, and in other types of insurance, this asymmetry can either occur in favour of the consumer or it can be in favour of the benefit provider.
One example that benefits the individual, can be the simple case of not providing key medical information or by lying about medical problems (e.g. lying about medical history) in order to improve your chances of getting a better premium under Health Insurance products. This is an example of fraud.
There are also 2 other forms of this which benefit the individual: Namely 'anti-selection' and 'moral hazard'. With anti-selection, individuals will have information that the insurer may not have and may act on that information such as by exercising an option which they know will benefit them. This can lead to a pool of people in worse health who are more likely to exercise the option. Moral hazard is a change in behavior of individuals as they are no longer fully exposed to the entire risk. Hence, individuals will often know more about their own actions and may choose to act on these actions knowing that they have medical cover.
An example that is not in favour of the individual might be due to the lack of medical expertise that individuals have. When assessing medical risks, individuals will tend to go for consultations with doctors who hold the expertise in order to improve their knowledge. Medical professionals hold significant power over our decisions, and there is a big informational imbalance between professionals and individuals, hence the decisions individuals make may not be fully informed if the medical professionals have inadequate expertise.
Another example might be the difficulties in comparing products across different insurers. The premiums may differ and you may assume that the product with the higher premium has better quality, but it can be difficult to assess the quality across insurers especially if the products are complex. The Insurers have more information than the individual, and can use this via marketing and sales to affect the individual's decision.