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In other words, it allows setting different variable values for each domain and for each language at the same time.
This module supports almost all of the functionality provided by Domain Configuration, Domain Settings and Domain Theme. Differences are listed in #1773702: Differences to domain configuration/settings/theme.
NOTE: If you need to have variables that are both multilingual AND domain variables, you must also enable the Domain+I18n Variables Integration sub-module.
Original story here: #1307058: Use new Variable API for different variables per domain.