Happiness has been foundational to ethics all the way back to Socrates, who believed that virtue was the greatest good, and that virtue was necessary for true happiness. This was later emulated by the Stoics, such as Epictetus, who argued that virtue was sufficient for happiness. The Cyrenianics and Epicureans both bypassed virtue and embraced a truly hedonistic ethical philosophy, where pleasure is the only good and is sufficient for happiness. All these ethical perspectives assume one thing -- that happiness, for some reason, is good. They all seem to suggest that something else is good in that it is a means to happiness.
Every ethical philosophy since then has at least something to say about happiness. Agreed, many have become ascetic, but I know of no ethical philosophy embraced by any that embraces asceticism for any other reason than to preserve happiness in either this life or the next. The utilitarian philosophers are clearly the most obvious modern proponents of happiness as the foundation of ethics, whereas Kant and other deontologists are probably the most obvious objectors to the idea, and usually replace it with duty and a respect for dignity or another seemingly independent and altogether desirable state of being besides happiness. This issue of whether or not a state of being can be both desirable and separable from happiness is fully worthy of a discussion of its own, but right now I want to focus on what happiness is, and what makes it so important in terms of ethics.
We all know what it feels like to be happy, but that doesn't mean it is necessarily an easy thing to define. The biggest obstacle in defining the term is that different states are experienced as "happiness" by different people. One person may be happy whilst getting whipped, while I would certainly not find that a state with which to be happy. But, there does seem to be a couple of key characteristics of any state in which any person would claim to be happy -- and they are the satisfaction of desires and a sense of tranquility.
First and foremost, for someone to be happy, the indulgence in and satisfaction of at least some desires is necessary. It seems impossible for someone to be happy whilst their most basic needs are left unsatisfied for long periods of time. A starving person is miserable and cannot do anything to improve that state until he has adequate nourishment. The same goes for the thirsty and the freezing. If you are not content and satisfied, you are an unhappy person. Even the Stoic's recognized this, despite believing the contrary in theory. In his Discourses, Epictetus poses the question, "Who then is a Stoic?" He tells his audience to show him "a man moulded to the pattern of the judgements that he utters, ... who is sick and yet happy, in peril and yet happy, dying and yet happy, in exile and happy, in disgrace and happy" (Discourses, Ch. XIX). He fully admits that you will find no one of the sort.
Something is still missing from the ingredients to happiness, as if one merely sought to satisfy each and every desire, one would likely be in a state that wasn't anything close to what one means by "happy." It would be the state in which the Cyrenianics pursued. But, happiness is almost certainly more complex than that, as a thoughtful reader should realize. People who seek satisfaction on a whim are often the least happy in that they are easily disturbed when their desires fail to be indulged. Instead, happiness is far more tempered and tranquil than that. It requires that one is relatively free from disturbances of any sort. Epicurus is perhaps the one ancient philosopher that I believe is closest to the concept of happiness that I am proposing. He taught that "pleasure is our first and kindred good," but that we "often pass over many pleasures when a greater annoyance ensues from them" and "consider pains superior to pleasures when submission to the pains for a long time brings us as a consequence a greater pleasure" (Letter to Menoeceus). In other words, the satisfaction of desires is the foundation of happiness, but we will avoid certain pleasures because they inevitably cause disturbances that cause us to be unhappy in the long run.
So, happiness requires that we feel both satisfied and tranquil at the same time, and is thus more or less the maintenance of a balance between a Stoic sense of calm and a hedonistic sense of indulgence. This is what happiness is, and as a matter of fact, it is deemed desirable by all those that have the even remotest ability to attain it. It is this very fact, that happiness is desirable (and, in fact, impossible not to desire), that makes it so ethically relevant.