One keyword can be tracked in many groups simultaneously. To move a keyword from a group or to add it to multiple groups, use the folder icon next to the keyword.
Note that keywords can only be added to regular groups, and not to smart groups or automatically created ones (like the Ungrouped or Brand).
When moving more keywords at a time, the whole batch can be handled using the options at the bottom of the keyword list:
This is also how keywords can be deleted. After deletion, you can always retrieve them in the trash bin, in Website Settings:
As a final tip, when you tick the "Select all" box, you can choose between selecting all of the keywords in the current selection or all of the available keywords (to save you from having to repeat the same action on every page):
Here's a video to guide you through the main available metrics in your SEO Campaign: