An arduino is a microcontroller with a few conveniences added. There are plenty of microcontrollers inside of devices that last for years on tiny coin cell batteries. You can program it to go into an ultra low power sleep mode and wake the instant you press a button or on a predefined schedule, do whatever business you want it to do for a few moments, then go back into ultra low power sleep. Some microcontrollers are more optimized for this use case than others, but plenty of ordinary ones are and they've gotten incredibly good at it.