What can I learn from a burndown chart?

Burndown is the estimated amount of work that remains to be done in an iteration, compared with the work originally estimated.

At any time, you can click on a planning folder and see how the sum of the estimated and remaining effort for all contained and descendant features is changing within a given timeframe. This helps you see how the estimates for your features are changing from day to day, and how the team is progressing towards "done" (remaining effort at zero).

You can use the trend line shown in your burndown chart to do some useful things:

The information you derive from your burndown chart will help revise the product scope, make accurate planning decisions, and refine implementation details.

Here's an example of a burndown chart.
burndown

In general, a burndown chart trends downward until it reaches zero. In practice, some events can reverse the downward trend of your burndown chart. For example, development work frequently uncovers a greater scope for a user story than was initially estimated. As a result, you'll revise your estimate of remaining work on that story, and your burndown figure may be pushed upwards.

The burndown chart uses whatever effort units you are using in the planning folder.

Note: The story told in your burndown chart is only as reliable as the underlying data. The owners of individual task artifacts can help keep the burndown chart accurate by regularly updating their remaining effort figures.