Jellyfish have a complex life cycle that includes both a sexual stage and an asexual stage.
In the sexual stage, the body (called a medusa) produces gametes (eggs and sperm). Then the eggs fertilized by sperm develop into a free-swimming larval form called planula.
After a brief period floating about in surface waters, the larvae settle to the sea floor, attaching themselves to a rock or the seafloor. They develop into a polyp (asexual stage) and begin to feed and grow.
In spring, some of the polyps start to bud off immature jellyfish known as ephyra larvae. These grow into mature jellyfish.
Yeah, it's definitely a bit unnerving.