Cardio (exercise) is basically good for your cardiovascular system (heart, lungs, and everything involved with moving oxygen through your system). The reason so many people look to cardio for weight loss or "getting in shape" is because it burns through calories. Weight loss is a function of calories in being less than calories out. The problem is that doing cardio for extended periods of time can cause loss of muscle. Additionally, if the cardio is running, it's pretty stressful on joints (especially knees).
That's why a lot of people are on the HIIT train (things like intervals/sprints). It allows for the benefits of cardio, less muscle wasting, and is lower impact.
I think the biggest advantage of strength training over cardio is that by doing strength training, you increase the amount of lean muscle mass in your body. This, in turn, increases your basal metabolic rate -- meaning you burn calories even when you're not working out. Cardio doesn't do this. In fact, it may slow your metabolism (due to loss of muscle mass). On top of that, muscle mass causes your body to look different. When people say they want to looked more "toned" what they really mean is they want to look more muscular (people just don't really understand what muscle looks like).
All that said, there's no reason to just do one or the other. You can (and should) incorporate cardio and strength training. That may be something that you add in later though. If you're overweight, I think the first thing you should do is fix your diet. Figure out how to count calories and learn how to manipulate what you're eating to lose weight. That link above is actually a really good overview of everything you should eventually know. The 80/20 rule is absolutely true, and that's why my other post where I said the majority of my time is spent on diet is so important. You can fuck around in the gym with a great diet and make progress. You can also have a workout routine that is absolutely 100% perfect for your body and a shitty diet, and you won't make any progress.
Anyway, once you've got diet figured out, incorporate strength training or cardio. Then later on add the other. If you try to do all 3 you'll spin out and quit.