First, all the disclaimers. I'm only doing some research here, using resources available to me. I'm not an expert and even though I'm a scientist by training, I'm not a cosmetics chemist and I don't work on beauty products or food for a living. Therefore, I'm not doling out any advice, and please don't expect me to do so. I was just very curious about the labels that are being tossed around and plastered on every product, so I went and did what I've been trained to do - look it all up.
"Organic," in the United States, at least, is "a labeling term that indicates that the food or other agricultural product has been produced through approved methods that integrate cultural, biological, and mechanical practices that foster cycling of resources, promote ecological balance, and conserve biodiversity. Synthetic fertilizers, sewage sludge, irradiation, and genetic engineering may not be used" (US Dept. of Agriculture site). In the United States, the National Organic Program monitors and regulates all organic crops, livestock, and agricultural products, making sure that they comply with a list of standards that are required to be fulfilled in order for the item to be certified "organic."
Now, that's just talking about food, and specifically in the US, as, to my knowledge, every country has its own specific standards set. I tried looking for FDA (Food and Drug Administration, in the US) comments about organic skincare, and found this FAQ page. The last question there really hit home with me: just because it's "all-natural" or "organic," (and those terms are not equivalent) doesn't immediately mean it's safer. Many people have food allergies, like nuts, for example; nuts are perfectly natural and can be raised and harvested in organic-compliant methods. (If you're curious about the FDA's regions of authority with regard to cosmetics, see here.)
The last thing on the poster is that the USDA doesn't regulate personal care products and cosmetics that don't claim to be organic, and also that other "private standards" (which can include "eco-friendly, earth-friendly," etc.,) are not regulated by a federal body. Which may or may not mean anything to you, but it's important to know.
So, before you start shaking your fists at me, let me be clear: I'm not suggesting you EMBRACE ALL THE CHEMICALS (even though everything, including dear old water, is technically a "chemical"), but I do caution against blind-embracing everything with a fancy label. Also, you may have noticed that I only used US descriptions and standards in this post. That's because I have no idea who or what governs products in your area of the world, and I don't have enough knowledge to make any sort of assessment there. I encourage you to do your own research, if you're so inclined. And if you find out anything interesting, please share! That's what the community is all about, after all.
 Ohloff, G., Pickenhagen, W., Kraft, P. Scent and Chemistry: The Molecular World of Odors. Zurich, Swizterland: Verlag Helvetica Chimica Acta. 2012.