The Auctiva store is just an alternative way of showing your eBay listings and store items.
Unfortunately it is not a replacement for eBay listings!
You don't have to have an eBay store but you have to have an eBay account and listings (including their fees!) to use the Auctiva features.
Auctiva is just an alternative to using the eBay listing forms, Turbo Lister, Selling Manager/Pro, etc. - it isn't a stand alone selling platform.
Until someone gets off their butt and creates a decent alternative to eBay, I think we're stuck with it. (Richard Branson are you listening?)