Paul's whole closing to this chapter/subject is about not giving a false witness to non-believers. If they are participating in idolatry and ask us to do the same, then to them we are saying what they are doing is okay. However, if they are not freely giving information on things being sacrificed in idolatry, we don't need to worry about it.
While the action being spoken of here is eating, the premise of the whole chapter is idolatry. In America, we don't really have too much experience with this concept as most of what we think about when it comes to idolatry is things people did in the past.
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