Q: Today, while visiting a few sites I use daily, a window asking me to enter my iCloud password showed up; obviously, I refused doing so.  Any idea why this is happening now?

Force Quit .

Press command + option + esc keys together at the same time. Wait.

When Force Quit window appears, select the Safari if not already.

Press Force Quit button at the bottom of the window.   Wait.

Safari will quit.

Relaunch Safari holding the shift key down.

Identify and remove adware/malware

http://www.thesafemac.com/arg/

http://www.thesafemac.com/mmg/

or download and run this Adware Removal Tool

http://www.thesafemac.com/art/

Please post a screenshot that shows what you mean. Be careful not to include any private information.

Start a reply to this message. Drag the image file into the editing window to upload it. You can also include text in the reply.

That's legitimate and probably indicates an attempt to access your iCloud Keychain. If it's persistent, see below.

Back up all data. Open the iCloud preference pane and uncheck the Keychain box. You'll be prompted to delete the local iCloud keychain. Confirm. Then re-check the box. Follow one of the procedures described in this support article to set up iCloud Keychain on an additional device. Test.