Not sure I've ever seen one of these before - but there were plenty on a particular tree I noticed when we visited The Dandenongs - perhaps they're quite common trees? This is another photo from the day we visited - 06 April 2013. I wasn't satisfied with any of the photos I took for this day. :)
Evelyn, there is a chestnut inside that burr. The burr is spikey and hurts to touch. It goes brown, opens slightly then drops to the ground. The chestnut is ready to eat when that happens. If they don't fall out when they hit the ground, use your foot to roll the burr along the ground and the chestnut will come out. Healthy to eat. Grown mostly in North East Victoria's alpine areas and of course in European countries. You may think I'm a smarty pants, but I only know this because my brother in law lives at Porepunkah and grows these trees to sell the chestnuts. Anyway, I really like your picture.