Organisms are any living things - giant trees, whales, mice, bacteria, penguins, people. Some people think the whole planet is a living organism which can regulate its temperature so that it stays just right for life to flourish. (This is called the Gaia Theory.) Organisms are alive and that means that they have the special power to be able to make endless copies of themselves - to reproduce. Genetically modified organisms (GMOs) are also alive and also have this endless ability to reproduce themselves. This is why many people think they are a very bad idea. Once GMOs escape from laboratories or farms, they can reproduce themselves and interbreed with non-GMO relatives and nobody can stop them. 
If something goes wrong with them (see genes), nobody can call them back. This is called bio-pollution which, unlike other pollution, cannot be cleaned up once it has happened. This is why protestors liken GMO escape to the tale of Aladdin and the magic lamp which he found. Once Aladdin rubbed the lamp, he released the magic genie. The genie, once released, was supposed to do Aladdin's bidding (like GMOs are for people) but suppose the genie liked being out? No-one could call him back!