Challenger Deep is the deepest point on Earth, and is part of the Mariana Trench. The Mariana Trench is in the Pacific Ocean, stretching from Japan to the middle of the Philippines.
Challenger deep consists of 3 pools, the Eastern, western, and central pool. The Trieste dove into the Western pool.
At that time, there weren't any accurate depth maps of Challenger Deep, so the crew used a technic where they set off explosives on the surface and timed their echo.