A genetically modified organism (GMO) is an organism whose genetic material has been altered using genetic engineering techniques. Organisms that have been genetically modified include micro-organisms such as bacteria and yeast, insects, plants, fish, and mammals. GMOs are the source of genetically modified foods, and are also widely used in scientific research and to produce goods other than food.

It's created a movement to label GMO food products.
The products getting the most publicity are corn, wheat, soybeans and other crops modified to resist the herbicide roundup.
Roundup-ready (RR) crops make it easier for producers to control weeds. For example see GMO and Monsanto Roundup: Glyphosate Weedkiller in our Food and Water? | Global Research

The claims are that no one knows what these modifications can do when you eat products containing them. And cross contamination of other non-GMO crops.

Articles:
Panic-free GMOs | Series | Grist
Genetically modified organism - Wikipedia
Bad science about GMOs: It reminds me of the antivaccine movement (revisited) Ð Respectful Insolence
More bad science in the service of anti-GMO activism Ç Science-Based Medicine