What do the 16 digits on a visa card mean?

Mostly, they are just an account number. Some of the digits, however, are "check digits." That is, they come from some mathematical formula being appled to some of the other digits. That makes it near impossible to simply make up a string of 16 digits that are a valid credit card number. Of course, the location of the check digits and the formula which generates them are carefully guarded secrets.