Push notifications and in-app messages are temporary which means that if the user has not seen them or he has dismissed them, he has no access to them anymore unless you have built a message center in your app.
An in-app message center (app inbox) can capture and store messages your users want to keep track of. Its implementation can complement your overall mobile messaging strategy.
Message centers generate better response rates. According to Urban Airship research, message center content generates 8x the read rate of push notifications alone. Also, message center read rates more than double when used in combination with a push notification.