>It was specified in Perfect Memento in Strict Sense that the spell card system was developed by Reimu Hakurei (however, the original draft being written on a youkai contract has called this into question) and first used in the Scarlet Mist Incident. They were designed to give even weak youkai and humans a chance to win, as well as to provide youkai a way to defeat the Hakurei Shrine in a fair duel. They are described as pieces of paper bearing the descriptions of their respective spells, along with the possible approval of the shrine maiden. This reason was explicitly used in Silent Sinner in Blue, where Marisa Kirisame convinced Watatsuki no Yorihime to use the spell card rules in order to make fights equal and, as Yorihime puts it, to prevent bloodshed.
>In Silent Sinner in Blue, Marisa Kirisame describes them in terms similar to a regular duel: You must dodge your opponents or be crushed by them. However, the difference between spell cards and a normal duel is that "the most beautiful one wins. It's a very mental contest." Reisen Udongein Inaba clarifies in Cage in Lunatic Runagate Chapter Six that "beautiful" in part means without dirty tricks. As it seems in the following, spell cards regulate rules for the time a duel is held such as: Used equipment, a time limit, winning and losing conditions and restrictions (mostly for the dodging part).
>Spell cards however don't seem to be limited to magic. Sanae Kochiya is able to call upon the power of a god, while Nitori Kawashiro or Marisa are able to use equipment, such as the Mini-Hakkero. Everything that can be used as an attack counts as a spell card, including everyday objects. Kogasa Tatara throws umbrellas in some of her spell cards while Minoriko Aki uses potatoes.
The actual spellcard rules say that duels between youkai would literally destroy Gensokyo, so that's why they were drafted.