Let's assume that the service is called "Throwbox", and you have an account with username `you@foo.com`, and the person you want to send a file to has username `them@bar.com`:
- You have a folder on your computer called "Throwbox"
- Inside that folder you create a folder called "them@bar.com" (so /Throwbox/them@bar.com)
- You put a file inside that folder.
- They create a folder inside their Throwbox directory called "you@foo.com" (so /Throwbox/you@foo.com)
- The file that you put in the folder on your machine gets copied onto the folder they created on their machine.
That way you don't need any information from them other than their username, and you can't send files to people who don't want to receive them. If you don't want to get files from another person anymore, then just delete the directory with their email address. And sending files is 2 way; if you want to send them a file back, just put it in the same place.