Kanban (agile) boards are visual representations of a workflow (roughly translated to columns) and the tasks (cards) that follow that workflow.
Boards bin statuses into columns but aren't always 1-1 eg. "Open","Reopened", and "On Hold" could all be binned under a board's "To Do" column.
Kanban boards are populated by saved searches (using JQL, examples follow below) that tell the board what cards to display. Quick filters are optionally used to further refine the cards displayed. Swimlanes are a third implementation of this search language that bin cards into rows.