The health stars are supposed to show you which foods are healthier - the more stars, with 5 being the maximum, the better... allegedly! The star rating is mainly based on the amounts of sugar, saturated fats, salt and fibre in foods.
The health star system was funded by the government, in partnership with the food industry (which would be a conflict of interest, like sugar manufacturers telling you that sugar is good because it's natural)... The doctor's association (AMA) was also involved, even though they have no training in nutrition or the effects of food on the body! And retailer associations were also involved in the system - why? what do they know about what's healthy or not?!
I agree that foods high in sugar are given low rating, because sugar causes weight gain, diabetes, dental issues, and inflammation, which is the cause of most chronic health conditions including cancer. This is why a lot of popular breakfast cereals only got 1-2 out of 5 star ratings, because of their high sugar and salt content, such as Nutri-grain, frosties, fruit loops, and crunchy nut corn flakes and many more.
However, the most interesting ratings occur in foods with fats, with all-natural and healthy butter only receiving a 1/2-1-star rating, and highly processed, chemical-laden, inflammation-causing, trans-fat filled margarine getting a whopping 5-star rating! How is this possible? Apart from the industry bias already mentioned, it's because they are still using pre-1960s dodgy research that said saturated fat causes heart disease when what was actually found as the cause was trans-fat! Hence anyone who says that saturated fats should be avoided hasn't read the much more recent research (as I have) which says the opposite - that saturated fats reduce inflammation, reduce body fat, and protect the heart, amongst many other benefits! However the saturated fat found in meats depends on what the animal actually ate - grain-fed animals will have a high content of inflammatory omega-6 fats (which cause weight gain and heart disease), while grass-fed animals will be high in omega-3 fats, the same healthy fats found in fish!
My qualified recommendation is to ignore the new food star ratings, and certainly don't base your choice of options from this ridiculous system, as it doesn't accurately identify healthy foods from junk foods. Remember that the best and healthiest foods you eat do not actually have labels or star ratings - vegetables, fruits, grass-fed meats and healthy fats/oils such as olive oil (not for cooking), coconut oil and butter!