Influenced Opens - The number of opens that occur indirectly as a result of a push notification. Every app open that occurs after a push is an influenced open, whether it is the direct result of a push or not.
Influenced opens are only calculated for a 12 hour window after the push was sent.
There may be some overlap of direct opens and influenced opens numbers, depending on the app and the users. Neither direct opens or influenced opens are related to each the other. Adding the counts together for direct and influenced open will give you incorrect results.