The character 或 is used today for the meanings "or", "either", "maybe", and "perhaps". Historically, it had the meaning of "region", and it is this meaning that characters like 國 and 域 derive from.
This original definition is reasonable given its composition; it has the dagger-axe radical (戈), and according to 說文解字, it signifies someone guarding territory:
从囗从戈,以守一。一,地也。
Therefore, it's unclear how this character could get its modern meaning. How did this evolution take place?