Advertorial is what Native Advertising used to be called. It's a fairly generic term and covers several advertising tactics.
It can be as simple as making sure your banner ads match your content (article about chicken feeding machines shows ads for the Ronco Chicken Feed Shooter®). Typically it's more layered (geddit? chickens? layers???). An advertiser pays the publisher to either publish something they wrote that makes themselves look good. Or a publisher's editor writes the piece for the advertiser. It's then presented on a page devoid of any mentions of competitors and will often link to other content that makes the advertiser look even better.
Often the entire page is co-opted to focus on the advertiser: the article, the ads, videos, the sidebar, the related content, polls, events, etc. The key point is that at first glance it should look like the publisher's regular content. The hope is that the reader will be engaged and influenced before they notice the FTC-required statement that the content has been paid for by Ronco Happy Fat Chicken International.
Native advertising is also sometimes placed alongside a publisher's regular content. And while labeled appropriately as "sponsored content" or "advertorial," it's appearance alongside the other content will draw more attention and add credibility.
Encourage your advertisers to provide content that goes beyond a marketing spiel and will appeal to your readers because it offers them something of value.