noun
brand; branding iron
Refers both to the burnt-in mark itself and the tool used to make it. Context usually makes the distinction clear.
牛に焼き印を押す。
Brand the cattle.
この焼き印は江戸時代のものです。
This branding iron is from the Edo period.
烙印 is more often used figuratively for a stigma or disgrace, while 焼き印 is primarily a physical brand.
Compound of 焼き (yaki, 'burning') + 印 (in, 'mark'). The exact historical derivation is straightforward; the word has been used for physical branding since at least the Edo period.