We should distinguish between “objective” in the scientific sense, and the philosophical sense. In the scientific sense, it merely means observable, with some small margin of error. Varlos V defines it in the philosophical sense, which is not really applicable to the OP (post-clarification).
The question is, why do people agree (as scientifically measured) on what is beautiful?
The answer is that it is evolutionarily beneficial to be discriminating – you must discriminate in mate selection, food selection, etc.
The side effect to being disposed to discriminate is that this creates a feedback mechanism. Preference itself is selected for, and at the same time, what is preferred is selected for. Sometimes, the preferences truly matter. For example, all the antelopes mate with the strongest buck. Sometimes the preferences don’t matter at all. For example, there are thousands of variations in coloring among coral reef fish; any specific coloration works as long as it distinguishes the fish. But the key trait is to have the ability to prefer.
When a species has the ability to choose based on a preference, then it can evolve quickly. With successive generations, any genetically possible trait that the species can imagine can evolve. Again, sometimes the preference ends up being crucial to survival, and other times, the ability to prefer essentially “treads water” producing arbitrary evolution.
Human beings recognize what is beautiful, in the same way that we recognize what is red, blue or green. Everyone can do it to some degree unless they are crippled. However, some humans have an exceptionally refined sense of what is beautiful, and this is called taste. If what they prefer ends up being evolutionarily beneficial, then that sense of taste is selected for. If it doesn’t, then it dies out. There is no reason why there can’t be various competing/cooperating tastes in one population. The balance is that if you are too discriminating, you won’t make a crucial selection (such as a mate). However, if you are just discriminating enough, and about the right thing, then your survival improves.
But without some basic notion of beauty, your offspring are doomed to stagnate, and that is why we all have it.