Swimming in the Dead Sea

Put the salt into the water (at least 4 heaped teaspoons) and keep stiring with a spoon until the salt is totally dissolved in the water.

If you place the grape into the water now, it will swim on the surface (see picture on the right).*
What has happened with the water? Why is the grape able to swim now all of a sudden?
To illustrate what is happening while putting the salt into the water, we will do another experiment.

*If the grape does not swim, you have to put more of the salt into the water.