Beauty is, according to Aquinas, “that which, being contemplated, pleases”. This, of course, is not a description of beauty as much as a criteria for beauty: it brings pleasure of itself. Compare that to a nice steak; it brings pleasure because it fulfills my need for food in an ample and satisfying way. But a sunset or a mountain does not. Beauty is about what the effect they make upon me, not whether they meet a need.
Does this make beauty entirely subjective? Yes and no. It is subjective in the sense that some people find something beautiful while others do not find those things beautiful. But this does not mean the concept of beauty is entirely subjective, that is, resides only within us and outside objects have no chance of displaying qualities that are beautiful in themselves. In other words, we all seem to have some notion of an agreed upon criteria for objective beauty; we may, however, disagree on whether a particular thing meets those criteria. But surely two people can disagree about whether a certain politician, for example, is honest or wise without concluding that honesty or wisdom are entirely subjective concepts. If there were no objective meaning of those terms, it would be rather pointless to argue whether a certain person was, in fact, honest or wise.
In the same way, I think people confuse subjectivity of judgment regarding beauty with subjectivity of criteria. Compounding the fact is that criteria may or may not be effable, that is, able to be put into words. This does not make them subjective, but merely points out that our language is not equally capable of describing all different kinds of reality.
In any case, those who have thought through the issue have usually concluded that things which we find beautiful share at least some of the following characteristics:
Let me comment on two of these.
The idea of radiance is difficult to fully describe in words. Aquinas uses the word “brilliance”. It is perhaps seen better than described. Compare a vivid sunset to a plain dusk.
The idea behind the ‘meaning’ criteria is that beautiful things often, and sometimes on a subconscious level, point beyond themselves. We see a high mountain and we think of majesty; we hear Bach’s Mass in B Minor and we think transcendence. We read the passion narratives and we are wrapped in wonder, shame and thanks all at the same time.
For theistic philosophers, we should add one other characteristic. This characteristic may fall under the category of meaning, but it is meaning of a particular kind. Theists believe that this world, even in its fallen nature, reflects God (though, because of the fall, does so unevenly). Natural beauty, then, is like a shadow of God’s beauty. In a sense, God’s beauty emanates out to natural things through His act of creation.