Professional tennis tournaments - and other sports, as well - are called "open" to indicate that any professional player may make an entry, although, of course, not all will be able to play due to tournament limitations (e.g., 128 men and 128 women tennis players at a Grand Slam event). A "closed" event is one in which the tournament invites only certain players to play; these players are usually higher ranked and/or popular with the public (n.b., this is true of amateur and college level tournaments, as well). Technically speaking, all professional tennis events that earn players points on the ATP (men's) or WTA (women's) tour are "open" events to prevent anyone from being excluded from an event and, thus, not having a fair chance to compete and earn ranking points and prize money. Thus, the word "open" is somewhat superfluous, at least as far as the tennis spectator is concerned, and is, ultimately, little more than a marketing ploy.
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Because anyone can play if they qualify.
The Major tournaments of the world, for many decades, only permitted 'amateur' entrants. Being a sport, to a degree, professionals were 'frowned upon' by the tennis fraternity of the world's major tennis organizations.
Finally, in 1968, the Major tournaments became Open to all people.
Before tennis was a professional sport on amateurs played. Some of the amateurs become professionaland were barred from playing. Then tournaments were made open 2 both. Hence where the term comes from.