Taking your resting pulse rate regularly can show an improvement to fitness (e.g. your RHR is 70, 3 months later it has dropped to 60). And as Skip and William rightly point out, it can help you track when you're under recovered or coming down with an illness (though you could do that by just listening to your body and taking it a bit easier if you feel run down).
HR is only one of many fitness indicators, and I personally don't think it's the best or most useful. But at the same time, it costs nothing to track it so if you feel like it, go ahead.
Actually comparing HR with other people is pointless as peoples heart rates differ widely (e.g. my RHR is lower than some professional athletes, yet higher than a guy at work who hasn't exercised in 10 years). In general you'd expect the average CF heart rate to be lower than the average sedentary person, but on a case by case basis comparisons are meaningless