Genetically engineered food is food that contains DNA which has been modified through genetic engineering. The modification could be the complete elimination of a gene, creating what is known as a "knock-out" organism, or it could involve the addition of a gene from another organism entirely.
A number of crops in the human food chain have been gentically modified for various reasons. Some, such as soybeans, have been made "Roundup Ready", a modification that makes the plants immune to the common agricultural herbicide RoundUp. The purpose of this modification is to allow the soybean plants to be weeded via chemical sprays rather than manually. Other crops, for example corn, have had a gene introduced that makes them essentially poisonous to insects that eat the plant. This modification, know as "BT" for Bacillus thuringensis, the gene donor, allows the farmer to use less pesticides. These are just two examples of a wide variety of modifications that have been developed.
In the United States, genetically engineered crops have not been well accepted by the public, and most are not formally approved by the Food and Drug Adminstration for human comsumption. However the genetically modified plants are used as animal feed, and then the meat, milk, and eggs of those animals are consumed by humans.