Well, the guide where stars are awarded was first published in 1900, as a guide for motorists to tell them where they could get fuel, food, and so on. It's developed since then, so that now you get separate guides for each country. The guide has kept going, and the 'Michelin' guide has evolved from a guide for motorists to a culinary award.
They - so far - have not been launched in America, although there is a New York guide and Chicago and LA coming.
Why are they so prestigious? Well, for one, very few restaurants get top marks. In the UK there are only 3 3-star restaurants. I think there are only around 50 in the world, France being the country with the highest number. For two, the 'Michelin' name and stars are very well known and respected. The loss of even one Michelin star can knock millions of euros off a restaurant's profit per year.
Finally, they are coveted due to the pride of top chefs. They aspire (as many chefs do) to get Michelin stars - aiming for 3 Michelin stars is the chef equivalent of your dream coming true.