From Webster’s Dictionary:

ORIGIN Old English, of Germanic origin; related to German Brand, also to burn¹. The word originally meant ‘burning’ or ‘a piece of burning or smoldering wood’ ( sense 3 of the noun); the verb sense ‘mark permanently with a hot iron’ dates from late Middle English. The noun sense ‘mark of ownership made by branding,’ based on the latter, arose in the mid 17th cent., and from it is derived sense 1 (early 19th cent).