The Iteration Burndown Chart is a graphical representation and projection of remaining unfinished work in that Iteration. In an Iteration, the Burndown Chart is located in the Reports tab of the Iteration Detail Page.
The start date and end date of the Iteration Burndown Chart correlates to the start date and end date of the Iteration.
Hovering over an individual day of the Burndown Chart will provide a count of actual Stories or Points remaining in your Iteration, and the ideal number of Stories or Points that should be remaining to complete all of the work in the Iteration by its end date. The ideal number of Stories or Points remaining is represented by a straight dotted line, starting from the actual stories remaining on the first day of the iteration, and falling to 0 on the last day of the iteration.
The Burndown Chart will also show much new work was added to the Iteration on that day, and how much existing work was removed from the Iteration on that day. Stories added during the Iteration's time period will be represented by a purple bar along the Burndown Chart, while Stories that have been removed during the Iteration's time period will be represented by a yellow bar along the Burndown Chart.
The setting for whether your Iteration's Burndown Chart displays its data in either Story Counts or Points can be configured in via the Story Count/Points drop down at the top of the Burndown Chart:
An Iteration's Burndown Chart will "freeze" once its end date has passed. If you are viewing your Iteration Burndown chart in Points, the Burndown Chart will reflect the current Points of the corresponding Stories, up to the last day of the Iteration. That is, if the Points Estimate of a Story in an Iteration changes after the Iteration has ended, it will not be reflected in the Burndown Chart. Similarly, if you are viewing your Iteration Burndown chart in Story Counts, the number of Stories added to or removed from the Iteration after the Iteration has ended, will not be reflected in the Iteration's Burndown Chart.