The differences between organic and non-organic produce can be kind of complicated and hard to understand. In short, organic foods are grown and produced using methods that do not involve synthetic (human-made) chemical fertilizers, pesticides, herbicides, or insecticides. According to the article "Organic Foods: Are they safer? More nutritious?" from the MayoClinic Website, conventional methods use these to promote plant growth, reduce pests and diseases, and manage weeds. These synthetic chemicals can be harmful to both human health and the environment. Organic methods of food production, on the other hand, use natural fertilizers (like manure or compost) for plant growth, birds and insects for pest and disease reduction, and methods such as crop-rotation and tilling to manage weeds. Read the full article for a more detailed explanation.
I wish that all the food I purchase could be organic. Unfortunately I don't have the budget for that. However, I try to find the money to buy at least some organic produce on each of my shopping trips. For example, I always buy my lettuce/spinach organic. My favorite brand of organic food is Kashi. I constantly have a supply of their snack bars and cereal in my room. My family loves it as too, so it's nice to be able to go home enjoy it there as well. Check out Kashi's website to find out more about the company and the different products they offer.
A friend and I took a trip to the "Topeka Natural Food Co-op" earlier this afternoon. They sell a wide variety of local, organic, and natural food and Earth-friendly products. I've never been in a store that is strictly natural and organic. I usually just shop in the organic section at Wal-Mart or Dillon's, so it was really fun and interesting to see! They have some foods there that I didn't even know could be made organic. I decided to splurge a little and purchase some natural wild-salmon burgers. I had one tonight, and it was delicious! I'd definitely recommend making a visit if you get a chance. Check out their Facebook page for more information!
In addition, the article "Organic Foods: Understanding Organic Food Labels, Benefits, and Claims" provides a great explanation of the harmful effects of pesticides and the many benefits of organic produce. It also explains how to read organic food labels, why organic produce is more expensive, how to stay within your budget while shopping, and how to choose the "right" organic foods.

This slideshow includes some pictures that I took at the Topeka Natural Food Co-op and pictures of Kashi products and other organic produce I currently have.