The Derived Data folder contains all the intermediate build information, debug- and release-built targets, as well as your project's index. It's helpful to delete the derived data when you have odd index problems (code completion not working right, constant re-indexing, or even just a slow project). Deleting the entire folder nukes this information for all projects Xcode 4 knows about.
The Archives folder (a sibling of Derived Data) contains the archived form of your targets. That is, a release build as well as dSYM data for later debugging. This you should not delete if you want to be able to debug deployed versions of your application.
You can nuke the derived data for a given project by opening the Organizer window and selecting the Projects tab. Select the desired project and click the Delete button next to the Derived Data path. This is more of a "surgical strike" for problem projects.