In tennis, two teams consisting of one or two players each face each other on a court that is divided by a net. The players use rackets to serve a ball back and forth between each other. The rackets traditionally were flat circular devices with strings, but later rackets were developed that were made entirely of metal. Points are awarded to a team when the other team allows the ball to go out of play or hits the ball into the net.
In the early 21st century, Melody Sawyer was the second-seeded tennis player at the Goddard Moonbase semi-finals. Years later, she would play both James T. Kirk and T'Lera of Vulcan in spirited matches. (TOS novel: Strangers from the Sky)
As a young woman, Kathryn Janeway played tennis quite frequently, and competed with others. At the age of 12, Janeway walked home over several kilometers during a thunderstorm because she had lost a tennis match. (VOY episode: "Deadlock"; VOY novel: Mosaic) Janeway gave up the game after playing on her high school's tennis team, and would not take up the sport again until 2373 when commanding USS Voyager - which was then stranded in the Delta Quadrant. (VOY episode: "Future's End, Part I")
Julian Bashir was also an accomplished tennis player in his youth, and seriously considered playing at the professional level, but would decide to instead pursue a career in medicine. (DS9 episodes: "Melora", "The Wire", "Past Tense, Part II", "Distant Voices")
As humans moved into the interstellar community, tennis became popular amongst other species as well, including Bajorans. The Bajoran Ibudan enjoyed playing tennis, and a calendar that Odo later reviewed showed that he had scheduled himself for several tennis matches. (DS9 episode: "A Man Alone")