What does "organic" really mean?

"Organic" means using less pesticides, or no artificial pesticides, and little or no GMOs. But standards vary widely across the world. Organic food product is, for the most part, a self-regulated industry with government guidance in some countries.

US Standards

The USDA National Organic Program creates standards for the US organic farming industry. But since the USDA is part of the FDA, and the FDA is well-known to be soft on GMOs and pesticides, the US "standard" is questionable at best. (March 2016: There is currently a lawsuit against the FDA for violating it's own regulations.)

The USDA NOP has the following areas of responsibility:

1. Manage organic operations. The NOP Intro to Organic Practices PDF is here.
2. Develop regulations and guidance on organic farming. CFR Regulations are here. The NOP organic handbook is here.
3. Manage the national list of allowed and prohibited substances. 
4. Investigate regulatory violation complaints. 
5. Accredit certifying agents. 
6. And a few more items. 
7. Here is a list of certified organic companies in the US and which products are certified organic. There are several fields to search on including company name, city, state, country, and certified products. 
8. Conform to regulations when exporting or importing organic foods.

How USDA NOP defines "organic" practices

1. Practices PDF here. 
2. Avoid use of synthetic use of fertilizers. Note that the US regulations do not ban synthetic fertilizers. But, nitrogen is nitrogen unless it's contaminated with something dangerous. 
3. Avoid sewage sludge* and biosolids. Sewage sludge can contain many toxic chemicals including heavy metals. 
4. Avoid irradiation and GMOs.
5. Use cover crops to reduce erosion.  
6. Use organic seeds unless that variety is not available as an organic product. In this case they can use non-GMO seeds.
7. Use crop rotation to reduce pests and diseases. 
8. Manage pests using Prevention, Avoidance, Monitoring, and Suppression (PAMS). Predatory insects are allowed. As a last resort the growing can use organic pesticides. I assume Bt is allowed in this case as it's a "naturally occurring organism" allowed by the NOP.
9. Organic crops must not receive overspray from non-organic crops if the farm grows both. 
10. Land that has had conventional pesticides applied cannot be used for organic crops for 36 months. 
11. More guidelines on animals are in the PDF.

* Sewage sludge is the sludge left over from sewage processing. Due to poor US regulations and interference from industry, sewage sludge can contain heavy metals and other toxic chemicals, some of which are absorbed by certain crops. From Wikipedia:

Class A sludge is typically dried and pasteurized, and is also known as "exceptional" quality. Class B includes all sludge not classified as Class A. Class B sludge is typically "undigested" and is volatile. Both classes of sludge may still contain radioactive or pharmaceutical wastes.

Now you know the basics of organic food farming.