According to mythology, the Titans were a race of powerful deities that were the predecessors of the Olympian gods.
The natives of Vagra II were described as a "race of Titans." (TNG: "Skin of Evil")
In 2375, after Solok presented a baseball challenge to Benjamin Sisko, Sisko presented the challenge to his senior staff as "a contest of courage, teamwork and sacrifice." Before knowing what the challenge even was, Julian Bashir "when is this clash of the Titans?" (DS9: "Take Me Out to the Holosuite")
The phrase "clash of the titans" refers to the Titanomachy, a mythical war involving the Titans.