Each pattern has 4 parts:

Name, which allows developers to speak the same language.

Problem, which describes when the pattern should be applied and in what context it is appropriate.

Solution, which is described in terms of the relationships, responsibilities and collaborations of the objects involved in the pattern.

Consequences of using the pattern, such as the costs and benefits of applying the pattern.

There are 3 types of design patterns:

Creational design patterns concern the process of object creation.  An example is the Singleton pattern which ensures that a class only has one instance, and provides a global point of access to it.

Structural design patterns deal with the composition of classes or objects.  An example is the Composite pattern which composes objects into tree structures to represent part-whole hierarchies and allows clients to treat individual objects and compositions of objects uniformly.

Behavioral design patterns characterize the ways in which classes or objects interact and distribute responsibility.  An example is the Observer pattern which defines a one-to-many dependency between objects so that when one object changes state, all its dependents are notified and updated automatically.

Patterns are language (and methodology) independent.  They can be used to capture common design practices, frameworks and architectures.  They are also being used to capture existing large legacy systems such as the 4E and GTD-5 switching systems (at GTE and AT&T) and to examine ways to re-engineer process and organizations (Coplien's Process and Organizational Patterns).

Patterns and Software Design.  Thus, when using patterns as part of software design methodology, we get the term used throughout this web - Design Patterns.