@Seamus: I think you are undercutting your point by the particular example you cite. Certainly Arturo Magidin's answer is an actual answer to your question. It begins:
"'Permutation group' usually refers to a group that is acting (faithfully) on a set; this includes the symmetric groups (which are the groups of all permutations of the set), but also every subgroup of a symmetric group."
That's the answer to your main question. He then goes on to provide additional insight into what's the point of saying "permutation group" when every group is a permutation group. (In summary, yes, every group is isomorphic as an abstract group to a permutation group, but the same group can be realized as a permutation group in multiple ways, some of which tell you a lot about the structure of the group itself, and some of which seem not to.) This is much more than just vaguely related to the question, and Arturo is not "showing off"; he is a research mathematician in the subject of algebra who is taking time out to share some of his insight.
This is an illustration of Qiaochu's point: the OP is not necessarily in a good place to evaluate all the answers to the question. However, the system allows for multiple answers and allows you to choose the one which you like best, which then gets displayed at the top, even if it is not the most popular answer in terms of upvotes minus downvotes.
Were you actually satisfied by the answer you accepted? If so, the system worked the way it should. If not, you should unaccept the answer and clarify what more you are looking for. Note also that although some people are going to pitch answers at a higher level and/or riff on things of interest to them, others will look carefully for clues as to the OP's background and use this information to craft an answer at the right level. (I think both of these practices are valuable, and I have done both myself in answering questions.) You can certainly help out the latter people by including as much relevant information about yourself, your general math background, and your math background specific to this question. For instance, based on your reaction to Arturo's question I am guessing that you are a beginner in abstract algebra, but your question did not convey that.