Unleavened bread is bread that is made with nothing in it to make it rise: that is, no leavening, be it a chemical leavener, a yeast or a starter dough.
Well-known examples are chapati, matzo and Mexican tortillas. Not all flat breads, however, are necessarily unleavened.
In Church services, Western Christianity uses unleavened bread, whereas Eastern Orthodox Christians use leavened bread
In Jewish cooking tradition, “se’or” means “leaven” and “hametz” means “leavened bread.” Five types of flour — wheat, rye, oat, spelt, and barley — can be mixed with water to create a starter dough. If the mixture sits for more than 18 minutes, Jewish religious tradition deems that is long enough for wild air yeasts to have infiltrated the dough, making it a starter dough, therefore a leaven. The mixture must be baked within 18 minutes.
Traditionally, corn wasn’t a forbidden Passover grain, because it wasn’t even known until relatively recently in Jewish history. However, it is now considered forbidden by custom. That’s why some Jews won’t use regular baking powder during Passover, as it contains some cornstarch. Special Kosher for Passover baking powder uses potato starch instead.
If you’re wondering why baking soda and baking powder are allowed at all during a time when only unleavened products are supposed to be eaten, it’s because some say that baking soda and powder are fine because the leavening is a chemical one, provided that the mixture they are in is baked within 18 minutes before wild air yeasts can begin to colonize the mixture.
Irish soda bread is not kosher enough for Passover, because its ingredients are together during the making for more than 18 minutes.