So what happens if you put a saltwater jellyfish in freshwater?
When the jellyfish is put into a hypotonic solution, such as water, there is a higher concentration of salt in the jellyfish. In order to balance out the salt to water ratio, water flows into the jellyfish.
This is a good example of osmosis. A process by which molecules of a solvent (water) tend to pass through a semipermeable membrane from a less concentrated solution into a more concentrated one. This equalizes the concentrations on each side of the membrane.
The jellyfish will take on water and become larger until it bursts.
When the jellyfish was in saltwater it was in an isotonic solution, meaning that the water to salt ratio was equal both in and out of the jellyfish. So water would move in and out of the jellyfish at the same rate without the jellyfish expanding or shrinking.
If the jellyfish was in a hypertonic solution with a higher salt to water ratio outside the jellyfish than inside, the water would be sucked out of the jellyfish in an attempt to create an isotonic solution. In the end the jellyfish would shrink.