What is a design pattern?Simply put a design patterns is well thought out solution to a common problem.
Design patterns has been around for a long time in software design. Ground breaking work was made by the "Gang of Four" in their book "Design Patterns". If you are a software developer you probably are familiar with the book.
UI design patternsSimilar approach can also work on user interface design. They can be especially useful in mobile UI design as problems with small screens can be emhasized.
UI design isn't exact science though. In my opinion UI design patterns are much more like frameworks for solving problems than ready solutions. They can sometimes be applied directly but more often than not they should be adapted to the needs of any particular UI that is being designed.
I've formalised the patterns in a bit different way from the Gang of Four book. I've selected problem, solution and consequences as the main properties of each pattern. See smartphone and tablet UI patterns.
When to use a design patterns?A design pattern should never be applied without a reason to do so. You should never try to solve a problem that doesn't exists. For example Dashboard Android UI design pattern, that is very widely used, does not apply to every app. If the app in question, for example, only shows next departures of a nearby bus stop the design probably should not have a dashboard landing screen.
Never use a design pattern that that doesn't solve a problems you have.Even if you have the exact problem described in a pattern description UI design patterns don't always work regardless of the app. It's always wise to evaluate use of any design pattern in the context of the app.
Benefit of using UI design patterns
Using UI design pattens also bring consistency to the Android platform. Users know how Action Bars and Dashboards work.
Another big benefit is availability of free library projects that help the developers get started with implementation much faster.
Read more about design patterns
Design Patterns, the book (software design patterns)
Smashing Magazine "40+ Helpful Resources On User Interface Design Patterns"