The little "balls" are the seed pods. They start off green and shiny and bumpy. They then grow and start to brown and open their little "eyes". Once they have ripened, they drop to the ground and become bare feet bombs - i.e. they hurt when you step on them in bare feet!
They attract lots of birds. While they are green, the various parrots (cockatoos, galas, lorikeets etc) feed on them in the tree. You have to watch the galas, as they tend to throw them at you if you are walking near by. Their aim is sometimes incredibly accurate! The cats (ours and a neighbours) won't go near the front yard while they are there!
Once the seeds fall to the ground, the lovely nesting doves feed underneath the tree. They are not afraid of the cats. They have their measure, keeping a wary eye on them and a specified distance from them. They seem to know what the cats can and can't do, as there has never been any casualties.