What does the leaf symbol in the status column of the task manager mean?

Notice that your process has a > in front of it? If you click it, it opens the group to see what's inside.

You'll notice that you find a new process in there with the same leaf icon. This time, however it also has the word "Suspended" next to it, which is the tooltip you were looking for,

These processes are suspended because they are not actively used. This means that the process is not using any CPU but can be resumed at a later stage to work again without starting up. Windows manages the suspending/unsuspending of its core processes to make windows respond more snappy but not actually run slower because there are background processes that aren't being used.

Do note, the faster your computer is, the less likely it is that windows needs to suspend processes. So some users with fast pc's may not see any suspended process, while people with a slower pc may see a lot of them.