The repository pattern is a design pattern that creates repositories of data that talk to a data source. These repositories are used to segregate the code that talks to a data source from the rest of your program. For example, your code that communicates to a database connection is stored within a repository class. Communication between your program and the database is all funnelled through the repository class.
In Domain Driven Design, you create data objects that are logical representations of the data stored within a data source; such as a database. These data objects may not mimic the design of a database, but instead be a more logical grouping of properties and methods. The repository pattern can be used to create a repository class for each data object, where that object can then be created, read, updated, or deleted (CRUD) from the data source.
Using the repository pattern with Dependency Injection allows for the repository class to be mocked during testing, where a more controlled and faster repository can be created. Also, if the data source changes to a XML file or another database, the repository class can be replaced.
The Repository pattern is one of the design patterns that I use to build a more maintainable and flexible application.