Positive psychology is the study of happiness. Psychology has traditionally focused on dysfunction—people with mental illness or other issues—and how to treat it. Positive psychology, in contrast, is a field that examines how ordinary people can become happier and more fulfilled.
Optimists have a tendency to make lemonade out of lemons, and to then see the glass as half-full rather than half-empty. It's an admirable quality, one that can positively affect mental and physical health.
Gratitude is an emotion expressing appreciation for what one has—as opposed to, for example, a consumer-driven emphasis on what one wants. Gratitude is getting a great deal of attention as a facet of positive psychology: Studies show that we can deliberately cultivate gratitude, and can increase our well-being and happiness by doing so.