6 of the links are internal, and 4 of the links are external. Page rank is passed completely proportionally, so 60 of your page rank points get passed to the internal pages you link to, and 40 get passed to the external pages you link to. This doesn't affect how the page with the 10 links on it ranks, but does affect the pages you are linking to.
So now say you add 10 more internal links to that page. You now have 16 internal links, and 4 external links.
Now 80 of your page rank points stay internal, and 20 go to external sites.
That's what he means by "conserving" link juice within your site.
Random example, there's 5 pages, page A, page B, page C, page D, page E that make up your site.
page A is the only one with any links going to it from outside websites. It therefore has 100 page rank points.
Page A has 1 link to pages B, C, D & E. So a total of 4 internal links. It also has 6 external links, to random websites.
In this scenario, pages B, C, D and E would each have 10 page rank points each. (So their share of the 40 page rank points kept internally). They have no more PR than this, because all their PR is gained from internal links.
Of course it quickly gets messy when pages are interlinked in a complicated manner etc.. But the general concept is the more internally linked your pages are, the better you are at keeping PR within your site.