A god box is where you write things down, problems you are facing, situations that are troubling you, or issues that you are dealing with. You can even just write a person's name on a piece of paper, or a post it, whatever. Then you put it in the box. This is a tangible way of "giving something/someone to God", handing something over. When you drop it in the box, you let go and let God take care of it. At one of our annual retreats alot of people bring their god boxes and at a special ceremony on the last morning of the retreat there is a big bonfire and everyone burns the whole box. Someone brings a bunch of new boxes to the retreat, so everyone can choose a new box. I have a cigar box as mine. It could be a pretty bag, or an old purse, or even a cardboard box. It can be something interesting, like an old jewelery box from a thrift store or something.
Alot of my papers in it only have one word on them, like "future" or "job", or just someone's name. I have a little post it pad in there with a pen, to make it even easier to write things down and toss them in.