Middle English seren, from Old English searian (intransitive), of plants, "dry up, to wither, become shriveled" (a sense now rare or obsolete), from Proto-Germanic *saurajan (source also of Middle Dutch soor "dry," Old High German soren "become dry"), from root of sear "dried up, withered" (see sere).
The transitive meaning "cause to wither, make dry" is from early 15c. The meaning "to brand, to burn by hot iron" is recorded from c. 1400, originally especially of cauterizing wounds; the figurative use from this, "deaden, deprive of sensibility" is from 1580s. The cookery sense of "dry or wither (meat, etc.) by application of heat, scorch the surface of" is recent. Related: Seared; searing.