Asymmetric information means that one party to a transaction or a relationship has a larger amount of relevant information available to them, than the other party.
One example is a hostile takeover bid, where the management of the target company will always have more information about the business they are working in, compared with the takeover bidder.
This is one reason why markets are not fully efficient in practice.
Another example is the difference in the information enjoyed by the owners of a business and its managers.
The managers generally have more information than the owners do.
This is one aspect of the 'agency problem'.