No feature defines the KDE 4 release series more than Activities. At the same time, no feature is so little understood -- Fedora even has a package for removing the desktop toolkit, which provides mouse access to Activities.
But, when you take the time to learn about Activities, you'll find them a natural extension of the desktop metaphor that just might help you to work more efficiently.
Activities are a super-set of Virtual Desktops. They don't replace Virtual Desktops -- in fact, each Activity can have its own set of Virtual Desktops if you choose. Instead, Activities are alternative desktops, each of which can have its own wallpaper, icons, and widgets.
The most common way to use Activities is to create one for each general task that you do. For instance, you might set up one Activity with all the apps and widgets that you need for coding or writing. Another desktop might have your web browser, email reader, chat application and other Internet applications. Yet another might be your dumping ground for articles that you want to read later.
Alternatively, you might set up Activities according to location, with different desktops for work, school, and home. At LinuxCon last year, Carl Symon showed me a screen shot of an Activity created by Aaron Seigo to plan his holiday, which included a To Do list, a calendar, links to online travel guides, a weather report for his destination, and other features connected to the trip.
These are only a few examples of the innovative uses people have found for Activities. What all these uses have in common is a move away from a single all-purpose desktop, and a greater emphasis on purpose than the traditional, application-oriented desktop. In this respect, KDE Activities are dramatically different from the features called Activities in GNOME, which are groupings of applications.
Moreover, GNOME's Activities are automatically arranged for you, while the whole point of KDE's Activities is to customize the desktop exactly the way you want.
Of course, if you choose, you can use KDE perfectly well as a traditional desktop, which is why some Fedora users get along happily without the desktop toolkit. However, for anyone for whom doing things their way matters, Activities are at least worth an investigation.
In every distribution that I've seen, KDE opens with only a desktop. If you click the desktop toolkit in the upper right corner of the screen, and select Unlock Widgets, you can add widgets to your desktop -- over 75, by my count, ranging from toys and notes to direct links and tools for starting Facebook and your favorite blogging site.
One of the most important of these widgets is Folder View. Each Folder View is an icon set, and you can add multiple Folder Views to your desktop, positioning them as convenient. You can also right-click on the desktop and select from the context menu Desktop Settings -> Layout -> Folder View -> Apply to have one Folder View become the entire desktop. By default, such a Folder View is the contents of your Desktop folder. But, by selecting from the context menu Folder View Settings -> Location, you can specify another folder.
At this point, you have a standard desktop, not much different than what you would have had in the KDE 3 or GNOME 2 release series. In other words, in the jargon of the KDE 4 series, you have a single Activity -- most likely a general purpose one set up for your most common tasks.
One way to add additional desktops or Activities is to use virtual workspaces. Go the main menu and select System Settings -> Workspace Behavior -> Virtual Desktops -> Different Widgets for Each Desktop, and you can customize each virtual workspace.
The trouble with this setting is that virtual workspaces don't display in the list of Activities. Also, customizing both virtual workspaces and Activities could get confusing unless you create strong visual clues with the wallpaper and color schemes. However, you could use this setting to add another level of organization to Activities.
To add another Activity, select Activities from the desktop toolkit. In the current 4.7 and the upcoming 4.8 release, this selection brings up a horizontally scrolling window displaying all current Activities. In early KDE 4 releases, this display was an overview much like the one in GNOME, and in Plasma Active, the KDE variant for tablets, it's a spinner wheel, but the features are much the same in all these presentations.