When you snooze mail, it will be hidden from the inbox until a later time that you have specified. When it reaches this time, the mail will return to your inbox as long as your app is running in the background.
Our improved snooze feature is local to the device, so this behavior is to be expected. In the future, this may change as we explore third-party app syncing via a service such as Google or iCloud.
Snooze is only available for iOS users at this time, but is part of our product roadmap for Android and we hope to roll out support for this feature in the future.