Having timezones is important because the increasing amount of international and also large country information traffic is way easier to monitor/coordinate. Having time standards is really helpful in this sense. Disadvantages are when people who write software don't fully understand all the implications and write software that doesn't or poorly handle this phenomenon.
The advantage of having the time zones is that they help us in coordination of activities across the world. Time zones for example help us plan calls and travels. The disadvantage about time zones is that there is always some little math involved in establishing particular times.