Output” refers to the type of finished image you need. In the past, your only option with film was either a print or negative. Today you can still have a print or “hard copy”. Although more and more companies don’t bother with having prints made, some still do, using them in their files as a hard copy back up as they would other important information.
As digital output you have two options; either a CD or e-mailed. I have found that more and more firms simply want me to e-mail them either a high resolution jpg file or size it for their web site or both. I guess whatever makes your job easier is the best way to go.
No matter what you choose, your photographer should keep a backup copy for at least 10 years. What kind of file? A TIFF file is much larger but will not degrade every time it is re-saved like a jpg file. However a large jpg file takes up less space (less than 2 meg compared to around 24 megs. I archive all photos as a TIFF file while in most cases a large jpg file will serve you well.