Something is begotten when it's been generated by procreation — in other words, it's been fathered.
A somewhat old fashioned adjective, begotten is the past participle of the verb beget, which means to father or produce as offspring. You might recognize this word from John 3:16, one of the most popular and most often quoted bible verses: "For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life."