Calligra refers both to a company and its project. As described on the Calligra Office website, which is run by the KDE open source community, the open source software suite was created by "a community of volunteers, with different skills, contributing to different aspects." (That means it's free!)
Representing an international development effort, Calligra Office is also highly vendor-neutral, meaning it works well with Windows, Mac OS X, Unix/Linux and more. It also means that inserting a spreadsheet into a word processor, for example, is that much cleaner.
Get a visual for each program in Calligra Office by clicking through this slide show, and linking to product information or user reviews.