A burn down chart is a tool to visualise progress against time.
A good metaphor is spreading a pile of dirt with a shovel. If you are tracking the remainder of the pile over time and plot it, you've got yourself a burn down chart. When the dirt is shoveled at a constant speed, the burn down curve will be linear. It's easy to comprehend that in this case it's very easy to make a prediction about when the job will be done.
Burn down charts are an easy tool to track progress in project management. The horizontal axis shows the progression of time while the vertical axis shows the amount of work remaining at every point. This is a number and by the nature of complex work usually an estimate. Common measures of work or effort left are story points, ideal days or team days.
In Agile software development, burn down charts are used to track the progress of sprints or epics. Tracking the actual against the ideal line is a good way of ensuring that the sprint or epic is on track. Remaining work is usually measured in story points. Whenever a piece of work has been done, the actual line will move down (burn down) the amount of story points that the work had been estimated as. Whenever the actual line hovers far above the ideal line it's an indication that reaching the goal by the end of the sprint or epic is at danger.
Burn down charts can be used to track any other numeric goal. Have a plan on how many cookies you want to eat this month? Capture it in a burn down chart and let this help you to stay on track! For more examples see the gallery below.