Emoluments is when the proceeds of something owned by the government goes to an individual. So for example, if we said all the toll collected by the government for a particular road or bridge goes to so and so, that would be an emolument. If a public servant started renting out rooms in the capitol building or the whitehouse, and took that money for themselves, that would be an emolument.

Tagging along with someone else to get a free plane ride, or to use your connection to a public servant to cut a deal is varying levels of corruption, but it's not an emolument.