'Vlei' is the Afrikaans word for a shallow depression filled with water, and the name 'Sossusvlei' strictly only applies to the pan that lies at the place where the dunes close in, preventing the waters of the Tsauchab River from flowing any further - that is, on the rare occasions that the river does flow as far as this. However, the whole area is now known as Sossusvlei.
During exceptional rainy seasons, Sossusvlei may fill with water, but normally it is bone dry.
The mud from the river stacks up at Sossusvlei and after some 1000 years the river searches its way through the next row of dunes. This is how the place called Dead Vlei was created, where the river used to drain away many years ago. Because of the lack of water all the trees in this valley have died, so the meaning of "Dead Vlei" becomes clear.
What makes the sight of the Dead Vlei so remarkable is that there is not even moisture enough for normal decomposition to occur. So all the trees here, though dead, have been nearly perfectly preserved for centuries!
(Info mostly taken from wikipedia)