In a gof book, a client is code or a class that uses classes in a template.
for example, from an abstract factory template with motivation:

Consider a user interface toolkit that supports many look-and-feel standards, such as Motif and Presentation Manager. Different views and sensations determine the various manifestations and behavior of widgets, such as scrollbars, windows, and buttons. To be portable according to the look-and-feel standards, an application does not have to hard code its widgets for a particular look and feel. Creating widget instances for widgets throughout the application makes it difficult to change the appearance.
We can solve this problem by defining the abstract class WidgetFactory, which declares an interface for creating each basic type of widget. There is also an abstract class for each type of widget, and specific subclasses implement widgets for specific style standards. The WidgetFactory interface has an operation that returns a new widget object for each abstract widget class. Clients call these operations to obtain widget instances, but clients are not aware of the specific classes that they use. Thus, customers remain independent of the prevailing appearance.
There is a separate subclass of WidgetFactory for each standard style. Each subclass implements operations to create a corresponding widget for appearance. For example, the CreateScrollBar operation in MotifWidgetFactory creates an instance and returns the Motif scroll bar, while the corresponding operation in PMWidgetFactory returns the scroll bar for Presentation Manager. Clients create widgets exclusively through the WidgetFactory interface and do not have knowledge of classes that implement widgets for a specific appearance. In other words, clients must bind to an interface defined by an abstract class, rather than a specific concrete class.
WidgetFactory also provides a dependency between specific widget classes. The Motif scrollbar must be used with the Motif button and Motif text editor, and this restriction is enforced automatically as a result of using MotifWidgetFactory.
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