“Religious” covers a lot of ground. Double-check me, but I think it’s true that the majority of Americans engage spiritual practices (e.g., yoga, mindfulness meditations, mystical connection with nature, sense of the Divine as the Ground of everything rather than an omniscient and omnipotent personality) outside the conventional Judeo-Christian frame, or are agnostic or atheist. It would be helpful at the outset to be clear what we mean by this word.
While the average religious person may be happier than the average non-religious person, that’s just about averages. Lots of religious people are unhappy, and lots of non-religious people are happy.
There is tons of science about how all people, religious or not, can affect their happiness. Basically, we can become happier by taking action in the world (e.g., doing crafts with your hands, giving to charity, planting a tree, getting a less stressful job, finding a loving partner), the body (e.g., losing weight, getting exercise, healing an illness, getting enough iron), or the mind.
While I can speak with authority on ways to boost happiness through action in the world or body, my expertise is the mind. In the mind, major factors that increase happiness include controlling negative emotions, controlling stress, savoring positive experiences (which defeats the negativity bias of the brain that makes it like Velcro for negative experiences but Teflon for positive ones), focusing on what one can do (how you’re like a hammer instead of a nail), positive self-talk instead of anxious or self-critical rumination, developing interpersonal skills that produce healthier relationships, gratitude, feeling connected with others, and feeling a sense of purpose and meaning in life.
Because of experience-dependent neuroplasticity – a mouthful that simply means that what we think and feel and want changes our brains – the mental factors and activities just above gradually build up strengths in the brain, much like building a muscle. The classic saying in brain science is: neurons that fire together, wire together.
The last three factors just above – gratitude, feeling connected to others, and purpose and meaning – are strong in most religious people, though of course they don’t have a monopoly on them. Your question hits the bullseye: what are the unique contributions of being religious to happiness?
A way to frame this could be, what can non-religious people learn from religious people about happiness? With a point made about how this learning can change the brain for the better.
Religious practice often involves a specific mental activity – focused attention on prayer or meditation: in other words, some kind of contemplative practice – that has good research on how it changes the brain. For example, Christian nuns recalling a profound spiritual experience and thus momentarily lighting up parts of their brains that control attention, tune into oneself, and feel rewarded. Or how the brains of long-time mindfulness meditators are changed in lasting ways, also building up layers of neural tissue in parts of the brain that control attention and tune into oneself. Non-religious people could also take up some kind of contemplative practice, even if they don’t think of it as religious or spiritual, such as meditation on the breath or really focusing on the body while doing Pilates, etc.
There is a lot of research coming out about the benefits of mindfulness training – outside a religious context – for controlling attention, improving response to medical treatment, and increasing happiness.
As a religious person myself – a Buddhist who believes in the Divine – I think there are certain aspects of religious life that you have to be, er, religious to benefit from, such as a sense of a personal relationship with God (by whatever name). I don’t know of any specific studies on this unique factor – though there may be some – but I can speak personally about it and report what others say, which is that it brings a sense of peace and joy.