When you attach files to your Podio app items, you can save different versions of the file using the "Replace file" tool. Previous versions of the file are available via the "previous versions" link, which will appear as soon as the original file is replaced.
You can read more information on adding files to your apps here. And learn about supported file types and sizes here.
Remember that all items in Podio have a change log, so you can always see who has edited anything within each item. Read more here.