At the top right hand corner of my iPad air, there is the pic of the book then the cloud and then the plus sign. My plus sign doesn't open a new page it closes the iPad? Help

When I tap on the + sign I get a page with all my bookmark folders. I can type a search or a web address in the address bar at the top, select one of the Bookmark folders or select a bookmark from the bookmark row under the address bar.

If you don't see these options but instead Safari quits back to the Home screen there are a few things you can try.

First thing to try is to reset your device. Press and hold the Home and Sleep buttons simultaneously until the Apple logo appears. Let go of the buttons and let the device restart. See if that fixes your problem.

If that doesn't help come back for more suggestions.

I have the same problem and resetting my ipad air did not help. When I hit the + sign safari quits and goes back to home screen

This post claims to have solved the same issue for the author:

https://discussions.apple.com/thread/5533964?answerId=23696850022#23696850022&tstart=0#23696850

Thank you this solved my problem!