Plastic bucket under gutter downspout
It's a strange method (to me, anyway) but my guess is someone put it there to prevent erosion. If you have water running from the downspout, without anything there it will basically pound a hole into the ground, as well as drain into your foundation, which can cause various problems including flooding of your basement, and cracked foundations. 





I guess it's the cheap equivalent of one of these:





It's best though to have an extension and get it far away from your house, so that water is running downhill/away from your foundation.