Not an expert, but the idea is that there should be some "thing" over which we can define functors which, after base change, are schemes.  Over this "thing", rings of integers should be literal curves.  The big example of things that I know is that a vector space over F_1 (or F_un, if you're the sort who likes fun notation) is a pointed set.  For more info, there have been some "This Week's Finds" posts about them, and also [this][1] series at neverendingbooks.


  [1]: http://www.neverendingbooks.org/index.php/looking-for-f_un.html