Consider this. Suppose I want to phone someone who lives in Japan and I live in the UK. Japan is +9 hours ahead of UK local time (GMT). Therefore I know if I phone slightly before lunch then I'll be phoning them in the evening.

Now suppose we all had the same time. If I phoned them just before lunch, which would mean shortly before 12:00 in the UK then I'd have to try and figure out what Japan would be doing at that time. Would 12:00 in Japan be early morning, late at night, would they be eating a meal, would they be at work? Now I have to remember where in the day different times are for different counties. However, with timezones all I need to remember is a numerical value and I can easily figure out where Japan is in the progression of a day (i.e morning, evening, night).