It's pretty obvious that water can hold up water. This obvious fact is exactly how floating works: if something is heavier than water, it sinks, if it is lighter than water, it floats to the top.
If you weigh a cup of water, and then weigh a cup of salty water, it turns out that a cup of salty water is heavier (denser). The more salt you dissolve, the heavier is the cup of salty water.
Salty water can obviously hold up salty water, that is it can hold up heavier stuff than plain water can.
Because the Dead Sea is much saltier than most of the world's oceans, and we are made mostly of water you can float in the
Dead Sea without even trying.
In order for you to float, the water that moves out of the way to make room for you. Since you are lighter (less dense) than water, the water pushes you up enough for you to float.
The Dead Sea has a lot of salt and other mineras in it. Salt water is heavier (denser) than regular water. People can float in regular water, but since salt water is even denser, it is even easier to float in the Dead Sea.