This is a way to introduce an opinion or fact that you think might make your listeners angry.

To "offend" someone means to say something that makes them angry at you. Here are some examples of things that you could say which would offend people:

• telling someone that they're fat
• talking about racial stereotypes
• expressing your negative opinions of women
• criticizing someone's idea in a meeting

If you have something like this which you know is going to offend people, but you want to say it anyway, it's common to introduce your sentence with "No offense, but..."