iOS had restricted multitasking exposed to apps for awhile (definitely by iOS 5) but it was restricted to certain kinds of apps: VOIP, background audio, newsstand, location awareness, or to a restricted period of time after the app is backgrounded.
They expanded it quite a bit in iOS 7? to all apps with background fetch, background url upload and download tasks, silent push notifications, and background tasks.
All of these approaches do not work if a user forcibly shuts down the app (I am not quite sure of every case). All these mechanisms are controlled by the OS: we'll call you, don't call us sort of thing and if you don't return in a certain period of time or if we need to, we will shut you down.
In iOS 8 you have extension support which launches mini apps. Extensions are somewhat equivalent to services but they are about integration with multitasking an implementation detail for security purposes.