What do I need to do when Facebook says: "Your computer needs to be cleaned"?

The message means that Facebook has received some unusual requests from your computer, like for example a large number of attempts to guess passwords for different accounts or attempts to post spam. So Facebook assumes that you have some kind of malware on your computer and recommends you to install a malware scanner to get rid of it. For more information check this article on facebook.com.

F-Secure and Trend Micro are quite well-known malware scanners, but not particularly better or worse than all the others on the market. Why does Facebook recommend those two? Only they know. Maybe they have an advertising deal, or maybe some admins at Facebook just like them. Whatever reason, when you don't trust the links provided by Facebook and don't trust my links either, just look up their websites in your preferred search engine.

However, Facebook can not know what kind of malware exactly you have on your computer, so there is no guarantee that these scanners will be able to find and clean it. And we have even less information about what malware you could have than Facebook does, so we can not offer you any advise except the usual procedure which will work on almost any malware: Format your computers hard drives, reinstall the operating system from scratch and restore your personal data from your backups. You do have backups, don't you?