It's a line chart that shows story points starting at the top left in the beginning of the sprint. Which shows all points to be done, trending towards 0 points with 0 days left in the sprint, in the lower right.
Linear means that the same points are done each day to allow the line to be perfectly linear between the top left and bottom right.
Remember the real goal: money. Sometimes it is money from sales, sometimes it is money saved. (even in case of a charity where there are higher goals money is a proxy for the real goal since it can be applied to the goal in some other way). If management can predict with reasonable accuracy when features will be done they can translate that into how much it will cost. Then they compare cost vs expected rewards (expected rewards is the job of marketing) and decide if they should focus on feature A, B, or both.
Note that many managers fail to understand error bars. There is no way to know exact numbers. However you can predict your likely error, and if the error is too high you can spend more money to reduce the error.
I recommend the book "how to measure anything" for more detail.
In the mean time when management wants perfect linear burn down charts, there is only one way to achieve them: overestimate your stories, finish them early and then go home. If you are paid for a 40 hour week you should average about 15 hours a week, but once in a while you will need to work a 40 hour week (60 hours every 10 years or so). Most management considers this unreasonable (for obvious reasons), but if a perfect linear slope actually is that important to them they will agree.
A pretty common burn down chart would have a somewhat linear slope in the beginning, a somewhat less sharp slope in the middle (mid-sprint slump), and a sharper decline to close out the sprint strong. Notice I said common (more likely to happen) and not ideal, because there truly isn't such a thing as an ideal burn down chart without context. What is ideal to one person/team may be completely different to another.
I personally track my time spent in an IDE slinging code or in app testing using an external tool to help me identify patterns. Purely in terms of time spent in IDE/app, Fridays are my least productive day by about an hour. Mondays are my second least productive. I am at my peak on Wednesdays. Thus I try to shuffle heavy loads to mid-week and the easy, gimme-task for Mon/Fri.
Just like a burn down chart, there isn't some ideal way productive time spent at work should appear on a graph. Well, I guess ideal is 100% of the day in IDE/app , but productivity would plummet. Humans just are not that efficient. Graphing my time gave me insights on how my week/month plays out. Burn down charts should do the same at a team level.