May be defined as changing an organism's DNA to make it more beneficial. It is important to notice that genetic engineering has been going on for a very, very long time in the form of selective breeding. However, actually going into a cell and changing its genome by inserting or removing DNA is a very new  technology.

Selective breeding has been going on for countless generations.
In fact, it is even mentioned in the Bible (Genesis 30:25 - 43). In the account, Jacob was employed as a shepherd under his father-in-law Laban. Instead of receiving wages, Jacob received the black, streaked, and spotted sheep, and Laban kept all the white sheep. Jacob craftily arranged for his black sheep to mate with Laban's white sheep, producing streaked and spotted sheep. Jacob did so well with this scheme that Laban's family began to get mad at Jacob, and he eventually had to leave. Some difficulties were faced.
Selective breeding is effective enough if the goal is to maintain or gradually improve a group of animals.
Over the decades, selective breeding has brought us improved strains of cattle and specialized breeds of dogs. However, these advances have taken hundreds of years to effect.
In addition to the time concerns, it is often impossible to know which traits will be transferred to the offspring.

Modern genetic engineering began in 1973 when Herbert Boyer and Stanley Cohen used enzymes to cut a bacteria plasmid and insert another strand of DNA in the gap.
Both bits of DNA were from the same type of bacteria, but this milestone, the invention of recombinant DNA technology, offered a window into the previously impossible, the mixing of traits between totally dissimilar organisms. To prove that this was possible, Cohen and Boyer used the same process to put a bit of frog DNA into Bacteria.
Since 1973, this technology has been made more controllable by the discovery of new enzymes to cut the DNA differently and by mapping the genetic code of different organisms. Now that we have a better idea of what part of the genetic code does what, we have been able to make bacteria that produce human insulin for diabetics (previously came from livestock), as well as EPO for people on kidney dialysis (previously came from urine of people in third world countries with ringworm).
In 1990, a young child with an extremely poor immune system received genetic therapy. Some of her white blood cells were genetically manipulated and re-introduced into her bloodstream while she watched Sesame Street. These new cells have taken over for the original, weak white cells, and her immune system now works properly.
Although relatively few people have had their cells genetically altered, these advances have made the prospect of mainstream genetic medicine seem more likely.
As of late summer of 1998, scientists are able to add simple traits to organisms. They cannot create custom-made animals. They cannot always predict how traits will interact.
Before phenomenally new advances can be made, scientists have to learn how to affect cells' DNA with high accuracy, without affecting other traits. Advances like genetic correction research for nearsightedness are a long way off.
The power of science is limited to knowledge about genetics, and trait interactions, but as knowledge grows, so will scientists' abilities to manipulate life. It is essential though to keep ethical prospective in the heart of every technology, including genetic engineering.