I was wondering, when the announcer says something such as, "This is German Shepard Dog number 7" what does the number 7 mean? I have some ideas but cannot find an answer anywhere. Thanks!

Each dog is entered under their breed with an assigned number. In the official book you would have (ex. ring 10 German Shepherds 5D 4B 9:15) Obviously the German Shepherds are showing in ring 10 at 9:15 and there are 5 male dogs and 4 female dogs competing.
When the handler goes to the table before going in the ring they will ask for the number corresponding with their dogs name.

Each dog is assigned a number when you submit an entry.
It is a way for the club to keep track of all the entries. So they assign a number to each dog.

Thanks everyone! I sort of figured that out last night when I finally noticed the announced number corresponded with the number on the handler's sleeve but this clears it up!

When you enter a dog show, you are assigned an "entry number."
This is supposed to keep things fair because the judge is not supposed to know the name of the dog or who owns it.
So for the entire time you are at the show, your dog is known to the judges by it's breed & number only.
The judges can't look at the "catalog" where the names of the dogs and their breeders & owners are listed.