The only time delay is used is when combining with animations. Typically used in conjunction with sequence to cause a delay before a second set of animations is run. This can also be used with super complex animations using sequence and parallel.

Like so

Animated.sequence([
  Animated.timing(this.state.colorAnimation, {
    toValue: 1,
    duration: 500,
  }),
  Animated.timing(this.state.scaleAnimation, {
    toValue: 2,
    duration: 300,
  }),
  Animated.delay(1500),
  Animated.parallel([
    Animated.timing(this.state.colorAnimation, {
      toValue: 0,
      duration: 500,
    }),
    Animated.timing(this.state.scaleAnimation, {
      toValue: 1,
      duration: 300,
    }),
  ]),
]).start();

Live Demo