The most common cause for file uploads not working are very large files being uploaded on a slow internet connection. While there is no file upload limit the server connection will time-out if the upload takes too long. This will result in the upload not being successfully completed. Things to try include reducing the file size by compressing images or editing videos, and trying the upload on a different connection, perhaps at your institution or place of work.
If you've managed to successfully upload your files into PebblePad but are struggling to use these files in your assets, it could be that there is a restriction imposed on the element by the resource builder - typically (and by default) media picker elements support only Image, Video and Audio files but can be extended to allow Documents such as PDF, doc, docx and txt etc but this would be down to the resource builder.