Dictionary.com defines the word "offensive" as: "–adjective [...] 3. repugnant to the moral sense, good taste, or the like; insulting: an offensive remark; an offensive joke."
Offensive material or behaviour may often be against common etiquette or classified as an expression which is against the rules. For example, the RIAA will take an offended attitude to those who consider copyright to be an offensive idea.
How we feel about offensive material may be determined by variations in culture, upbringing, and education. For instance, childrens' shows in Japan have depicted nudity, however, pubic hair is considered obscene. Meanwhile, in the US, the depiction of an erect penis in any media is considered obscene and is relegated to NC-17 fare only.