This answer refers mainly to KDE4. For Plasma 5, see update at the end of answer.
Terminology is relative, but I guess the term "Activity" is used instead of "Desktop" because the latter is more commonly used on the one hand when referring to desktop environments, and on the other when referring to "virtual desktops" or "workspaces", while Activities are a way of using the plasticity and mobility of KDE.
What are Activities?
Each Activity is a set of virtual desktops (workspaces) with specific characteristics.
There are different types of activities.
(Not only you can create multiple ones and switch between them, but their characteristics can be very different, because they are of different types.)
What can I do with an Activity?
Before knowing what you can do with each type of activity it is useful to know what each activity can do.
The different characteristic of an Activity/set-of-workspaces that is already in place can be specified by clicking the last entry of the desktop menu (right-click on desktop) inside that Activity.
There you will see different types of activities, under Layouts:
In different systems they may be more or different
Changing the layout changes in fact the way an Activity operates.
Similar options can be set when creating a new Activity, only they are inconsistently called 'Templates':
That also may vary
There are some inconsistencies:
- the template "Photos Activity" is absent from the list of "layouts". (So, you cannot set that "layout" to an existing activity, but you can set it as "template" to a newly created one)
- the template "Desktop Icons" is absent from the list of layouts, but it seems to do be same thing as the item named "Folder" (present in both layouts and templates)
Some of them seem to serve basically the same purpose (which will reduce the number of "types" available - see below), others seem to serve no purpose at all :) - but there are a few that are interesting enough to make this discussion worthwhile. Some of them are just empty plasma desktops with some widgets added by default but some are more fundamentally different.
There is also an option called "Get new Templates" when creating a new Activity, which should give us more types of activities, but that doesn't work in the KDE system that I tested.
What can these types of activities do?
I'll try to describe each type of activity (and I'll try to update this answer on the way).
"Folder" layout/template (not different from "Desktop Icons") shows the content of
~./Desktop and thus allows icon files on the desktop. Sending an application to the desktop creates just an icon file for that instead of an icon widget (as is the case in the classic KDE desktop layout).
The template "Search and launch" which seems to be the same as the layout called "Default Desktop" adds a very interesting feature: just by typing you can search and launch an application or search and find a file, bookmark, etc., without the need for clicking a search button on the panel or use a shortcut to open the search window. The search window pops up just by typing.
- "Homerun" creates a dashboard with main tabs that give access to the favorite items, the installed applications and the folders
Not present by default in Kubuntu 14.04
sudo apt-get install plasma-widget-homerun-kicker plasma-widget-homerun
"Group Desktop" has the option of creating groups, which look like empty widgets... What they are for I don't know yet.
"Grid Desktop" does the same as the previous, only it adds a grid on which the groups can be moved - but for what purpose I cannot say.
"Photo activity" is a classic KDE desktop that starts with two widgets (Photo Frame and Folders) showing the Pictures folder. Switching to this activity by shortcut will give easy access to your photos etc
"Newspaper layout" is (on my system) just an empty KDE desktop . It is just a name I guess with the idea of adding some widgets focused on news.
There can be many activities created at the same time, with different purposes, as the other answers explain.
But what I find interesting is to show the main types of activities that can be used and how they are different.
First, there are the widget-based activities: the classical KDE desktop layout (the one with icon-widgets, created by selecting "Empty desktop" for a new Activity) that can be by itself o good base for creating new specialized activities, by using specific widgets ("Photo activity" is an example).
Then, there are the three activities that have a different structure than the classical KDE layout+widgets. They all allow widgets too but add something more:
- access to the Desktop folder ("Folder"/"Desktop icons")
- "type-and-launch" feature ("Search and launch"/"Default Desktop")
- dashboard ("Homerun")
UPDATE on Plasma 5
In Kubuntu 15 the list of layouts contains only two entries:
- Desktop - Plasma empty desktop
- Folder view - access to
There are no Templates.
The default desktop has the "Search & launch" feature integrated.