I'm unsure if iPhoto is suggesting I rebuild my library. I only noticed the icon as I clicked on the top of my iPhoto screen in order to move it to the side of the desktop—it appeared just next to my cursor, so I thought perhaps I initiated a rebuild through clumsy use of the mouse, it seems unlikely but possible.
My wife did have trouble opening iPhoto the day before, maybe that's what triggered a rebuild and it only came to my attention when I moved the iPhoto screen.
I have iPhoto version 9.4.3, and the "Rebuilt Library" icon is on the desktop.
Interestingly, when I closed iPhoto in order to perform the option startup, I got the spinning beachball and had to force quit—when I reopened, using the option key, a window did ask which library to use—I chose the rebuilt library.
I moved the "Rebuilt Library" icon to the iPhoto Library folder.