One of the biggest and most persistent myths in agriculture is that the organic label means food is produced without the use of pesticides or other chemicals.
Just like conventional farmers, organic farmers can and do use pesticides to grow nutritious and safe food for human consumption. Generally, organic farmers are allowed to use most pesticides that are naturally-derived, while they are not allowed to use synthetic pesticides. The difference can sometimes be quite technical–some pesticides can be exactly the same except for how they are produced. In addition, there are some synthetic pesticides that are also allowed in organic production. You can view the entire list compiled by the USDA here.
Of course, agricultural pesticide use is regulated by the Environmental Protection Agency (EPA) so that all food produced is safe from dangerous levels of pesticide residue.