In this case,
Real Madrid stands for "Royal" Madrid... there are other football clubs in Spain that use the adjective "Real" in their names, such as Real Betis, Real Celta de Vigo, Real Mallorca, Real Oviedo, Real Sociedad, Real Valladolid and Real Zaragoza.
Winners of 8 European
Champions Leagues: 1956, 1957, 1958, 1959, 1960, 1966, 1998 and 2000. Winner of 3 World Club Cups: 1960, 1998 and 2000. Winner of 2 UEFA Cups: 1985 and 1986. Has also won the Spanish Cup 17 times and the Spanish Primera Liga 27 times, finishing as runners-up 15 times.