This pattern is all about interfaces.  It is, therefore, hard to summarize the interface issues in two paragraphs.  However, the key point to understand is that the adapter implements the target interface and so exposes methods which are useful to the client.  This is an interacting interface which the clients will access since they should be able to switch seamlessly between interacting with a class, which naturally exposes the target interface and an adaptee which exposes the target interface through the adapter.