late 12c., from Old French cort (11c., Modern French cour) "king's court, princely residence," from Latin cortem, accusative of cors (earlier cohors) "enclosed yard," and by extension (and perhaps by association with curia "sovereign's assembly"), "those assembled in the yard; company, cohort," from com- "together" (see com-) + stem hort- related to hortus "garden, plot of ground" (see yard (n.1)). Sporting sense is from 1510s, originally of tennis. Legal meaning is from late 13c. (early assemblies for justice were overseen by the sovereign personally).
"woo, offer homage," as one does at court, 1570s; see court (n.). Related: Courted; courting.