...for this to work as an SEO thing, there is a links page, but its just not visible to site visitors, ie it exists purely for the benefit of search engines?
Link farms can hurt your site ranking.
The number of backlinks a site has is not nearly as important as the quality of those backlinks. Ideally, you want back links from sites that focus on the same or similar keyword phrases and categories that your site uses. To accomplish this, you’ll need to have a great site that attracts links from other high-quality sites.
"Free-for-all" (FFA) sites do not constitute quality links, so don't waste your $24.95 submitting your site to 1,000s of them.
And when you're trading links, make certain your link IS visible to humans. If it's not, it's a link farm.
Google's SEO Starter Guide (PDF)
Thanks Nancy - the tool I'm looking at is Link Assistant - so the idea is that you find all potential sites to link to based on keywords or competing sites, and it has all sorts of data on Google Page Rank etc, so in theory flagging up good sites to get linked to.
I did miss originally that the tool does list pages where the links are no longer present (and flagged as such), so it was throwing me when I clicked through to a page, and saw no sign of a link.
The site I'm looking at actually does pretty well in Bing and Yahoo for its most obvious search term (digital photo frames) - making it to the first page.
The problem is Google, where its more like page 5-7. So the trick is to somehow figure out what Google seems to like, that Bing and Yahoo is less fussed about.