A single leaf holding one thing at a time. From the papyrus sheet, and beneath that from the verb to scratch - a card is a surface marked so it can be read.
Old French carte, from Latin charta (a leaf of papyrus, paper), from Greek khartes (a papyrus roll), itself traditionally connected to kharassein (to scratch, to engrave) — the same family that gives 'character'; a card is, at the root, a single scratched-and-readable leaf.
A single leaf holding one thing at a time — the same papyrus root that gives this house's paper, read here in its smallest, most portable unit.