Bloodstone is a dark green chalcedony, a variety of jasper, spotted with red iron oxide. The green is from chlorite and amphibole inclusions, the red spots from hematite. Physically it is unremarkable: an opaque, tough, common material, easily carved, historically cheap.
Its other name is heliotrope, sun-turner, and the classical explanation is worth recording because it is so odd. Pliny reports that the stone, placed in a vessel of water, turns the reflection of the sun blood-red; and that magicians claimed that combined with a particular herb it conferred invisibility, a claim he treats with contempt as the sort of thing the magi say. The reflection effect is describable as an actual optical observation of a dark green stone in water; the invisibility is not.
The famous association is Christian and it can be dated to within the medieval period rather than to antiquity. The legend holds that bloodstone was formed at the Crucifixion, when blood from the wounds of Christ fell on green jasper at the foot of the cross. On the strength of it the stone became a martyr's stone, carved with scenes of the Passion and with the flagellation in particular, and a large number of such carvings survive from the fifteenth and sixteenth centuries.
The legend does not appear in the classical sources, which know the stone under a different name and a different story. It is a Christian reinterpretation grafted onto an existing material, and the graft is visible: the pagan optical wonder and the Christian relic-substitute coexist in the medieval literature without being reconciled.