what does an offensive word mean ?

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i watched a reality show on tv a few days ago i seldom watch the show before, and it's quite interesting to watch as i watched yesterday, i can see that there's one of the cast who became the center of everyone the other casts dislike her, as she often acts arrogant also say something sarcastic once one of the casts argued with her, and told her for being 'offensive' all the time hmm, i wonder what would that offensive word mean ? girls fight are always interesting.. haha LoL does anyone here have the experience with people that you can describe as an 'offensive' one ? thanks for sharing .. ^^