Practically every item/component/circuit in electronics has practical applications otherwise they wouldn't exist.
We've had this question posted recently: "What are some examples of applications of a capacitor?"
Someone could ask the same question of a diode, transistor, gate, flip-flop, register, counter, multiplexer, decoder, etc.
Understandably, one has to learn about basic components and circuits before moving on to specific applications. In time, you will get to see the big picture.
What is a sequence generator? A sequence generator is a controller that defines specific tasks to be performed in sequence.
Think of the various functions and tasks that must be performed in a laundry washing machine - cold/hot water solenoids, drain valve, agitate, rinse, spin etc.
In a digital computer, instructions are acted upon in a sequence of fetch, decode, execute cycles. This is controlled using a sequence generator.
Those are just two examples of how a sequence generator could be applied.