The Marianas Trench (more commonly called the Mariana Trench) is the deepest trench, and contains the deepest point, in the ocean. The trench is 1,554 miles long and 44 miles wide. It is found in the Pacific Ocean east of the Philippines.
Its deepest point is called the Challenger Deep, and lies about 7 miles below the ocean surface. Filmmaker and explorer James Cameron made history in 2012 when he became the first human to solo to the Challenger Deep in a submersible.
The Marianas Trench is part of a system of trenches throughout the ocean created where the plates in the Earth's crust collide. The Marianas Trench is deep because it is located in an area of heavy, old (geologically) seafloor, where one plate (the Pacific Plate) is forced under another (the Philippine Plate), creating a trench. This area, far from any rivers, isn't covered in sediment like the floors of many other oceanic trenches, making it even deeper.
For more information on the Marianas Trench, see the Mariana Trench profile here.