What are "Photo Stream" events in iPhoto? They seem to have redundant copies of all my other photos, but bundled into month groups?

I have iCloud turned off in iPhoto. But maybe I used to have it turned on.

Are the photos copies? Or just pointers to other photos?
You may have had it turned on in the past. 

Go to System Preferences>iCloud and remove the tick to the left of Photos if it's there.
This will switch off Photo Stream if it is still on. It is also explained if you click on the 'options...' button on the right of Photos icon.