You should talk to your network administrator regarding this issue.
If you are the network administrator, then when you drew from all your
knowledge and experience to thoroughly and competently assess the issue
before you posted this question, you observed that the pop up balloon
appears when printing from any application, not just from Word, so you
accurately concluded that the setting that controls the pop up balloon
is more likely to be found in Windows than in Word. Hence, you
appropriately posted your question in one of the Windows newsgroups,
instead of in this Word newsgroup where your question would be
off-topic. And being the consummate professional you are, you have
developed sufficient written communication skills to include basic but
vital information in your question such as what versions of Windows and
Word you are asking about, because you realize that we can't see your
screen from here.
If you have Windows XP, then click on Start | Control Panel | Printers
and Faxes | File | Server Properties | Advanced. The bottom two to four
options relate to print notifications. Uncheck the ones you don't want.