Heroku does not support file uploads. The filesystem is readonly. You'll have to host your uploaded files somewhere else (or from the database, which is a bad option).
https://devcenter.heroku.com/articles/read-only-filesystem
Amazon S3 is a common choice: http://devcenter.heroku.com/articles/s3
If you are using any gems like paperclip or carrierwave for uploading, using S3 will be simple. You will have to set the S3 credentials in a config file and the gem will take care of uploading and will provide urls for the uploaded file.