A badge number is a unique number, often serial, assigned to and printed on each badge.
It's very useful to make each badge uniquely identifiable. If it's turned in to Lost and Found, you need some way to figure out who it belongs to, and if you observe somebody wearing it behaving badly, it's useful to know whose badge they stole at least.
If the names are pre-printed on the badges, this can be done by simply indexing all the names (though you have to do something about duplicates). However, at-the-door badges are rarely pre-printed, and getting the names on those badges into the list prepared in advance in a timely manner during the convention is also dificult.
So it's very common to put numbers on the badges, and use those as the unique identifier.
It doesn't particularly matter if you assign the numbers in order as registrations are recorded, alphabetically at the end of pre-registration, or even at random. However, changing a well-established practice at your particular convention is likely to attract attention and comment.
It's very common to reserve some low numbers for special people, particularly the Guests of Honor. It's very common to make sure the author guest gets badge #1. Alternatively, the ConChair may have badge #1. It might be socially prudent to also give the conchair's spouse a fairly low-numbered badge in that case. Other individuals may request particular badge numbers that are special to them. Whether or not such requests are satisfied is entirely up to the registration dept.
People often assume the badge numbers serve as a rough guide to the number of people registered for the convention.