There's something called a "genome" which maps traits of an organism. Biologists have been studying this for some time now, and Genetic Engineering refers to the theory that we can manipulate traits in an organism to create a creature that we designed from the ground up.
Advantages: We could, in theory, create a perfect being. We could get rid of genetic diseases...such as diabetes, by wiping them from the genome. We could, and this is all theory because there are moral issues surrounding this, create a sheep with angel wings and horns that had super-human intelligence and could spit fire. (An exaggeration but you see the point)...
Disadvantages: Nature has evolved since the beginning of time...and creatures have survived and reproduced based on their abilities to survive. It's called evolution, I'm unsure of whether or not you're familiar with it but it's a theory a man named Charles Darwin had more commonly known as "Survival of the Fittest". Scientists believe that introducing genetically altered organisms to the world could have CATASTROPHIC effects on the environment. Nature is balanced between predators and prey...and if you for example introduced bears that shot laser beams from their eye sockets (Comic Relief...don't take that literally)...they could essentially wipe out the entire deer and salmon population.
Here's a site that may help if I didn't explain well enough: