Array methods are built-in functions in programming languages that allow developers to manipulate and interact with arrays, which are collections of items. Common array methods include push, which adds an item to the end of an array, and pop, which removes the last item. Other methods like map and filter enable developers to create new arrays based on existing ones by transforming or selecting specific elements. These methods simplify tasks such as searching, sorting, and modifying data within arrays. By using array methods, programmers can write cleaner and more efficient code, making it easier to manage and process collections of data in applications.