If there is one thing in this world that the whole humanity is after, knowingly or unknowingly, it is Happiness. If this is more explicit in the human beings, it is instinctive in animals. For example, when thirst, hunger, etc. are satisfied the animal is in the state of a well being. So, we can explain happiness in animals this way - lets say, the deer is quite thirsty. After a long search, suppose it finds the water. When its tongue comes in contact with the water and it starts gulping the water, from one's own experience, we could easily imagine the state of the deer's mind. That's what we call the happiest moment. Why touching the water, even seeing the water from a distance, the state of mind is said to be quite happy.
So from this hypothesis, happiness can be defined as the process of satisfying the (instinctive) want / desire.
Happiness = Satisfaction - Want
Thus in animals, the want/desire is of the instinct nature so happiness is the process that ensures that the body is always brought back into the state of well being - a state of homeostasis at the body level. The instinctive wants are generated, and the whole system of the animal works to satisfy the wants. Again, after a while the same want is regenerated and the entire process continues till death. This is what we call (animal's) life! If you carefully observe, it is not just the want and the satisfaction. There is another entity in between the two for the happiness to happen. From the time of the generation of the want till the satisfaction, the animal is undergoing the state of stress, a difficult situation that we call suffering. So the entire process towards Happiness is Want --> Suffering --> Satisfaction.
Happiness = Satisfaction - (Want + Suffering)
( where, the result of this equation can be >= 0 )
However, in case of human being, there is another dimension added: psychological aspect of being. Since the brain & the nervous system is well developed, it makes the man a thinking animal and therefore the mind plays a major role in human being than in animals. In terms of capability Man is therefore = Animal + Evolved Mind. Thus logically speaking, human being's happiness can said to be a constant process of satisfying bodily needs (homeostasis) plus psychological needs, ... only adding to the complexity!