The genome of an organism is all of its genetic material, and the genes in it carry the instructions for its characteristics. Genetic engineering is a process in which the genome of an organism is modified, usually by adding a gene taken from another organism, so that it gains a desirable characteristic. This works even between very different species because they all use the same genetic code.
Bacteria can be given the human gene for insulin, so they make insulin that is used to treat people with diabetes. Crop plants can be given genes that make them resist pests or that make them more nutritious. In golden rice, new genes make the grains produce beta-carotene, which the body uses to make vitamin A.
Genetic engineering is different from selective breeding. Selective breeding picks parents with useful features and takes many generations, but genetic engineering changes the genome directly, in one step, and can use a gene from a different species.