As noted in the Honeygain application on iOS, you need to keep it running in the foreground in order to share your traffic and earn credits for it, however, what does the "Foreground" mean?
Foreground is the opposite of background. Running the application in the foreground means to keep it running as if you were actively using it.
For example, when you are watching a video on your iOS device, you are actively engaging in the video application that you may be using. Same goes for games or writing messages - you are actively using the applications and are keeping them running in the foreground.
Thus, in order for the Honeygain application on the iOS to share traffic, you would need to keep the application running as if you were actively using it (as if it was playing a video and you were watching it).
Tip: there is a power-saving mode on the Honeygain application for iOS. By turning it on, your screen would be dimmed, but the Honeygain application would continue to run in the foreground. This is useful in case you would like to keep the Honeygain application running throughout the night, but do not want your phone to be lit up.