noun
A mark burned onto something, often livestock or criminals historically; also used figuratively for a lasting stigma or label.
牛に烙印を押す。
Brand the cow.
彼は犯罪者の烙印を押された。
He was branded a criminal.
焼き印 is a more general term for a branding iron or the mark made by one, while 烙印 often carries a stronger figurative sense of stigma.
From 烙 (burning) + 印 (mark). The exact historical derivation is uncertain, but the spelling is conventionally associated with the meaning of a brand or stigma.