Kanban is an agile development method which uses cards and boards to visualise production as a series of tasks and sets rules on how those cards can move or be marked completed.
A kanban board usually consists of several columns, such as Backlog, Inplay and Ready for Review, and team members word on one card at a time. As tasks are completed they are moved to Ready for Review, or if blocked (because they need input from another team member to finish) they are marked as such. Sometimes they are also prioritised by a producer, although in some teams developers are trusted to handle their own prioritisation.
Kanban usually works very well as a day-to-day process for managing a project, but less well for strategic planning. Used solely by itself what often happens is that teams descend into pure maintenance mode, completing tasks but without a sense of stewardship or direction.