Cancer

It means Cancer, the crab sign, in astrology. In Western astrology Cancer is the fourth sign, a water sign ruled by the Moon, and is associated with home, family and protectiveness. In a bio the Cancer sign labels someone's star sign; in a compatibility message it names the sign being discussed. Sent alone, read it as astrology first — not as proof of flirting.

Where does the ♋ shape come from?

It stands for a crab, but its exact derivation is uncertain. The crab comes from the constellation Cancer, one of the twelve zodiac star groups that Babylonian astronomers mapped along the Sun's yearly path and Greek astronomy inherited. The compact curl-and-dot glyph came much later, in medieval astrological writing; its two curls are commonly read as pincers, though no one recorded what the scribes intended.