Saffron is one of a handful of natural products that's proven useful across history in number of different categories. Dye, spice, medicine, aroma therapy, anti-fungal, tomato plant fertilizer, currency... the list goes on. That said, we here at the farm primarily use saffron in one of two ways.
The truth is that almost all rare compounds have at one point or another been associated with health benefits. Rhino horn, bear bile, pangolin (scaly anteater), etc all fall into this category. Fortunately, modern science provides a clear distinction between superstition and reality in the form of the statistically significant trial. The idea here is to randomly separate your test subjects into two groups, giving one the treatment (eg saffron), and the other a placebo (eg sugar pill). We then measure the average difference between the treatment and control groups to identify the treatment effect. If the populations are large and the treatment effect is strong, science allows us to claim a statically significant benefit of the treatment. It's these sorts of trials that form the backbone of modern medicine and nutritional guidelines.
In the case of saffron, there are thousands of claims for everything from hair regrowth to mental clarity. But limiting the scope to just the statistically significant claims, we have:
Anti inflammatory - Inflammation causes swelling and pain, and saffron is a natural alternative to artificial NSAID.
Antioxidant - Fights against oxidation stress on your cells which in turn helps fight some forms of cancer.
Digestion - Long used as an herbal remedy for everything from an upset stomach to digestive track diseases.
Mood - Saffron aids in the boosting of serotonin levels, providing an alternative to chemical antidepressants and reduces PMS.
Aphrodisiac - Sorry folks, we're a wholesome family farm, so you'll need to read about this elsewhere.
Weight loss - Curbs appetite which in turn helps fight obesity and diabetes.
If you want more information, I suggest you start by reading this and this articles. They both provide a broad foundation of saffron as a medicine and are written from a scientific viewpoint.
Saffron is one of the primary food seasoning of the Middle East, India and North Africa. It's the ingredient that gives those foods a natural yellow coloring and exotic floral flavor. It's not as common in Western culture for historical reasons, but at some point neither was coffee or pepper and now who can live without them?
Personally, my favorite way to enjoy saffron is in black tea with cream. Throw in 5 threads at the start of your next brew for a whole new way to enjoy this classic drink. In my opinion, its subtle flowery and earthly flavor requires no extra sweeteners.