What is the difference between indirect evidence and direct evidence?
One good example is a voter’s list. Since a person has to be a citizen to vote, your ancestor’s name appearing on a voter’s list is indirect evidence that your foreign-born ancestor naturalized (assuming that the guy on the voter’s list really is your ancestor and not another guy with the same name). The evidence is indirect because the voter’s list doesn’t explicitly state that he was naturalized.
If the voter’s list is one of those that lists date and place of naturalization for voters, then the voter’s list would be direct evidence of his naturalization because it is specifically stating that he was naturalized.
Of course you ancestor could have lied about his citizenship status in order to vote, but that gets into accuracy of information which is a separate issue.
Indirect evidence can be more involved than in this little example, but this gets to the heart of the matter.