A Hint is an extra piece of information or a clue that Networkers can send to users regarding a mission.
Networkers will send mail when befriended, asking for some sort of favor. This is usually to allow the user to complete the campaign you are undertaking. If replied to with the "Could you please give me a hint" message under the blue "For Networkers" section of the mail, they will often send a clue of what to do next, such as an extended to-do list or some Blueprints that help in the Rank.
Not all Networkers give a hint. If they do not have a programmed response, they reply with the default message of "I don't get it" through the MLN Mail.