This may be a stupid question but, isn't hay just dead grass that's been baled.
No, not a stupid question at all. Hay is indeed dried vegetation that has been baled for convenience of storage, but it can be a complicated issue. Hay can be made of many different plants--unimproved meadow hay may have a wide variety of "weeds", such as yarrow, goldenrod, or various daisy family members; legumes such as clover, and various types of grass. Legumes such as clover and alfalfa provide high protein, but alfalfa is prone to woody stems and small leaves that shatter and fall easily. Even plain old grass has different nutritional value based on the stage of growth and even the time of day.
After cutting, if the conditions are good, farmers often get several more crops of hay from the same field. The first cutting is often stemmy and brownish, as it is often too wet and cool in the spring to cut and dry hay properly. Those who wait until the 4th of July to bale hay due to wet/cool conditions often only get the one crop of hay for the year, and it is often of poor quality as the grass has already gone to seed, as low as only 5% protein, and not much vitamin content as the grasses are already bleached out.
Second and third cut hays are usually much greener, shorter, and leafier, about 6-8 weeks of fresh, new growth. Cut early in the morning, as soon as the dew dries, it will have maximum sugars in the leaves, making it extra palatable to the livestock. Dried quickly and thoroughly, baled dry and stored dry out of the sunlight will make the best possible hay product.
There's actually a lot that goes into making good hay. Hay that is baled damp can develop a deadly mold. If you see clouds of white 'dust' coming from your bale when you open it, be very concerned. If the hay has a musty smell, be very concerned. Good hay is a delight to rabbits. They'll often eat poor quality hay and straw just for the joy of chewing it (you can tell when the straw filled nestbox is empty the next morning. Straw, by the way, is the dried stem of the mature grain plant after the grain has been removed--could be oat straw, rye straw (good for making straw hats), rice straw, etc.)
So, there's a lot that goes into good nutritional hay. We feed mulberry leaf hay as a treat, made from dried mulberry leaves, with a protein level around 15%..