How important is a heart-rate monitor?
The short annswer is not at all important. 
People trained and got fit for decades without heart rate monitors. Current thoughs in some camps is to dump heart rate altogether. For someone just wanting to get fit and loose some weight, heartrate monitoring is usually an interesting distraction. The drive for it comes down from pro level sports to trainers and manufacturers selling 'extras'.  

Unless you know you maximum heart rate (The 220-age formula is wrong as often as its right - do not use it), a monitor gives little useful information, and is more likely to put you wrong. You also need your aerobic threshold for it to anything more than marginally useful. Its very hard to establish aerobic threshold without knowing average heart rate, but you also need to know a lot more than just average.....

You should use the watch during training to ensure you are in your target bands- just look at the watch occationally. The proviso is  that you can accurately establish the correct heart rate bands. If you have a trainier, averages, time in band etc might help them tune your training program, but if you had a trainer, they would tell you if this is needed.