The @State keyword is a @propertyWrapper, a feature just recently introduced in Swift 5.1. As explained in the corresponding proposal, it's sort of a value wrapper avoiding boilerplate code.
Sidenote: @propertyWrapper has previously been called @propertyDelegate, but that has changed since. See this post for more information.
The official @State documentation has the following to say:
SwiftUI manages the storage of any property you declare as a state.
  When the state value changes, the view invalidates its appearance and
  recomputes the body. Use the state as the single source of truth for a
  given view.
A State instance isn’t the value itself; it’s a means of
  reading and mutating the value. To access a state’s underlying value,
  use its value property.
So when you initialize a property that's marked @State, you're not actually  creating your own variable, but rather prompting SwiftUI to create "something" in the background that stores what you set and monitors it from now on! Your @State var just acts as a delegate to access this wrapper.
Every time your @State variable is written, SwiftUI will know as it is monitoring it. It will also know whether the @State variable was read from the View's body. Using this information, it will be able to recompute any View having referenced a @State variable in its body after a change to this variable.