Hay is basically grass clippings bundled together to feed to grass-eating animals when there isn't any.
Great care must be taken to collect hay when it is as dry as possible and store it in such a way as to dry it further and keep it dry because wet hay rots. Decay produces heat, and because hay is also a great insulator that heat can even reach the ignition point for the dry parts of the hay.
It tends to smolder, since it is predicated on being fairly wet at first and the middle where it is hottest will have bad airflow until the whole "being on fire" part dries the rest out, but it will set your barn on fire easily enough, and it's a real devil to put out, since you're usually trying to spray water through dozens of feet of hay to where the core of the problem actually is.