Periodic background synchronization

There is an iOS feature called BackgroundFetch, which you can set up for

regularly downloads and processes small amounts of content from the network

You can setup a minimumBackgroundFetchInterval.

In contrast to the mentioned Android feature, this interval is not guaranteed though.

The OS does some heuristic in a blackbox. It rewards you for using a "reasonable" (to the OS) CPU time/ power consumption and also for being used often by the user. On the other hand you get punished for draining the battery or (even worse) never being used/opened by the user.

See: Apple Sample and Apple Docs

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Update: Since iOS13, BackgroundFetchis deprecated.

There is a similar, new API named BGTask, BGAppRefreshTask is the equivalent to deprecated BackgroundFetch.

See Apple Docs

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Alternatively, depending on your needs, you can post a Silent (push) Notification whenever the users data changes on server side. A silent push wakes up your app without notifying the user, so you can fetch data and maybe inform the user by scheduling a local notification.

See: Apple Documentation