This is a good link that explains the difference between organic and non-organic. Organic is thought to be better for the soil and environment, but "No conclusive evidence shows that organic food is more nutritious than is conventionally grown food. And the USDA — even though it certifies organic food — doesn't claim that these products are safer or more nutritious."
Organic foods: Are they safer? More nutritious? - MayoClinic.com
Organic can even harbor harmful bacterial, such as e-coli because manure is considered organic. All fruits and vegetables should be rinsed thoroughly before eating. If you can afford it, buy organic, but if you're on a budget non-organic is probably okay. For things like dog foods, this would not be a primary factor in my choice; in fact I would be suspicious of a company who used the word.
But that's just me . . .