A graben is an elongated, relatively depressed crustal unit bounded by faults on both sides. This geologic structure was first described in German, thats why the German term Graben (ditch) is used internationally as the geologic term.
A graben is caused by a divergent movement of the plate. The plate widens and becomes faults, which results in a downlift of the crust between two of the faults. This kind of structure is also called rift valley.
Once the graben is deep enough, sea water will flow in and the graben becomes a new sea, slowly but continually widening. The Dead Sea graben is in the stage just before the sea flows in. The Red Sea is a graben which is already filled with sea water.
After a continuous development the sea will become wider and wider, with a volcanic rift in the middle. This is how the Atlantic Ocean looks today. The rift is the Mid Atlantic Ridge, which forms a huge S, parallel to the eastern coast of the Americas and the western coast of Africa.