There are two properties:
significantLink - URL - One of the more significant URLs on the
page. Typically, these are the non-navigation links that are clicked
on the most.
significantLinks - URL - The most significant URLs on the page.
Typically, these are the non-navigation links that are clicked on the
most (legacy spelling; see singular form, significantLink).
Source: Schema.org webpage documentation
I agree that it doesn't explain what search engines will do with that data, but that's the point. Schema.org does not specify how things will look in search results: they only specify what something means, and leave it up to search engines to implement ways to display that data in a meaningful way.
Does google do anything with this, though? No, google has not completely implemented schema.org in their search results, and they don't have to. Here's the list of google supported schema.org specifications:
Google supports rich snippets for these content types:
- Businesses and organizations
Google also recognizes markup for video content and uses it to improve
our search results.
Source: Google webmaster support's page on rich snippets (microdata, microformats, and RDFa)
I don't see anything there about
significantLinks, so I'm going to conclude that google does nothing with it.
However, I don't think that google is going to implement this. This feature could easily be abused by people wanting certain pages to rank higher than others, even if they aren't relevant to the search query. If Google implemented this, it would destroy their user's search experience, and that's something I can't see google doing.