Basically genes or DNA code for amino acid sequences that lead to proteins and ultimately to whatever trait is associated with. The DNA code is universal with some few rare exceptions in some bacteria and viruses do some weird things with DNA. The same nucleotide sequence whether in an amoeba or a chimpanzee will code for the same series of amino acids. Therefore the idea of jelly fish DNA, or human DNA, or canine DNA is a bit misleading. The particular sequence may be associated with that animal, plant whatever but DNA is DNA no matter where it comes from.
A GMO is a organism that has its DNA artificially modified with a DNA sequence from another organism to impart that trait onto it. Say you discover a plant that has a resistance to a common herbicide. You can put that same gene into commercial crops to make them resistant to it, spray that herbicide around, and kill the weeds without harming the crops.
The fact that you imparted a gene from another organism onto a new one doesn't cause any health concerns on the crop or organism nor render it radioactive and eating it will not cause you to turn into a teenage mutant ninja turtle. It is a lot of hype and hysteria cooked up and perpetuated by people completely ignorant about biochemistry.