Before we get to the science, let me explain what "GMO" even means. It stand for Genetically Modified Organism(s). GM food, or GMO food, is food produced using genetically modified plants or animals. The phrase "genetically modified" may sound scary, but it shouldn't. If you've ever eaten beef, you've ingested a product of centuries of genetic manipulation. Cows aren't wild animals--they are domestic animals bred from their now extinct ancestor, the auroch. The animal we know of as a cow was created through careful breeding, a practice known as animal husbandry. Similarly, most of our crops bear little resemblance to the plants we bred them from. Thousands of years of careful selection of seeds and deliberate pollination to get desirable traits have led to the crops we grow today.
What activists are objecting to in GM food is the method of altering the genetics of the food organism is a bit different. Instead of cross breeding similar plants or animals to get desired traits, scientists are carefully inserting a single or a few desired traits into the plant or animal. These are traits that probably couldn't have been bred into the animal or plant because they come from a different species (animals and plants can only produce offspring with members of the same species). So, these combinations, though far more precise than the old fashioned breeding method, do introduce traits that probably couldn't have been produced in a "more natural" fashion. For more on this, let me suggest the following article that covers the matter in a bit more detail: Labels for GMO Foods Are a Bad Idea
Now that the basics are covered, it makes sense to ask if this newer method of modification is safe. The overwhelming body of scientific evidence says it is. From the article, "2000+ Reasons Why GMOs Are Safe To Eat And Environmentally Sustainable":
Every major international science body in the world has reviewed multiple independent studies—in some cases numbering in the hundreds—in coming to the consensus conclusion that GMO crops are as safe or safer than conventional or organic foods. But until now, the magnitude of the research on crop biotechnology has never been cataloged. In response to what they believed was an information gap, a team of Italian scientists summarized 1783 studies about the safety and environmental impacts of GMO foods—a staggering number.If you're interested in this topic, I'd encourage you to read the whole article. There's no credible evidence, no peer-reviewed study that proves any danger to humans or animals from GMO foods. The handful of studies I've seen that linked GMO foods to anything negative were junk science done to support the anti-GMO activists. They've been discredited and/or retracted.
The researchers couldn't find a single credible example demonstrating that GM foods pose any harm to humans or animals. “The scientific research conducted so far has not detected any significant hazards directly connected with the use of genetically engineered crops,” the scientists concluded.
Science is ever evolving. It's always possible that at some point in the future we'll find something wrong with the food we eat whether it's GMO or bred the old fashioned way. However, so far as the science can tell today, GMO foods are as safe as or safer than traditional crops.