Basically, this means the product you are buying is at least 95% organic unless 100% organic is specified. This usually applies to items that are mixed with others. In the case of coffee, it is one single crop so it is almost always 100% organic.
Organically grown means almost no chemicals were used. There is actually a list of approved chemicals that can be used as well as a list of substances that are banned in order for something to be considered organic. One of the stipulations on the list of substances means it must not harm the soil or water.
In order to be certified, farmers must demonstrate their entire growth and harvesting process. Once this is complete and they meet all the requirements, they can obtain the certification and earn the right to stamp that label on the side of the packaging.
Many believe that natural production methods ultimately produces a much higher quality bean. This makes organic coffee much more attractive to high quality roasters and shops as well as consumers looking for the ultimate coffee experience.