Community Wiki is a flag that can be applied to answers (and sometimes questions) which lowers the barrier for editing and prevents any rep gain/loss from voting.

See also:

* [What are “Community Wiki” posts?](https://meta.stackexchange.com/q/11740)
* [Privileges - Edit Community Wiki](https://mathoverflow.net/help/privileges/edit-community-wiki) in help center

An answer can be made community wiki by the post owner. A question can be made community *only by moderators*, see also the discussion here: [Community Wiki in the hands of moderators](https://meta.mathoverflow.net/q/448).

It is probably also worth mentioning that community wiki is (currently) used on MathOverflow slightly differently than in the rest of Stack Exchange network (at least in some cases). Some more details on this can be found, for example, in these discussions:

 * [Why was my non-big-list question made community wiki?](https://meta.mathoverflow.net/q/3853#3862) 
 * [Question mysteriously becoming community wiki](http://mathoverflow.tqft.net/discussion/247/question-mysteriously-becoming-community-wiki/?Focus=4242) (on tea; [Wayback Machine](https://web.archive.org/web/20151031151418/http://tea.mathoverflow..net/discussion/247/question-mysteriously-becoming-community-wiki/))
 * [When should questions be "community wiki"?](http://mathoverflow.tqft.net/discussion/6/when-should-questions-be-community-wiki/) (on tea; [Wayback Machine](https://web.archive.org/web/20160324190752/http://tea.mathoverflow.net/discussion/6/when-should-questions-be-community-wiki/))
 * Generally in Stack Exchange network the use cases described in the above discussions are discouraged, see for example: [The Future of Community Wiki](https://stackoverflow.blog/2011/08/19/the-future-of-community-wiki/) and [Stop using community wiki as a reputation denial mechanism](https://meta.stackexchange.com/q/227290).