The Adapter pattern allows incompatible interfaces to work together by converting the interface of one class into another interface clients expect. The document describes an example where a BotLeader interface with a fireBullets() method needs to work with a Ralph class that has a smash() method. An Adapter class is created that implements the BotLeader interface and contains a Ralph object. The Adapter's fireBullets() method calls the Ralph object's smash() method, adapting the Ralph interface to the expected BotLeader interface. This allows different classes to work together even if their interfaces don't match directly.