Pairing is simple, and exactly what it sounds like: two people working together on a single task or problem. Usually in this scenario, one person is the driver, who leads the task, and the other is the navigator, who reviews the code and provides input.
The intention of pairing is to create a tight feedback loop between two people working on the project. Ideally, this results in a particular task getting accomplished more quickly with less potential for error.
Pairing is also beneficial when two people of different disciplines work together. For example, a developer can work with a designer, a UX expert, or a product manager on the client's side. Another good scenario for pairing is when the task at hand is expected to be particularly difficult or prone to error. When people work alone on issues like these, it's easy to get frustrated, or take longer than is necessary to work around it. If the path seems unclear, two travelers are often better than one.
The team as a whole actually benefits as well. Pairing helps us gradually improve our craft and work faster, even as individuals. Pairing supports cross-pollination of knowledge and builds stronger relationships between team members. That's why it's a practice we tend to keep around.