An Advertorial is advertising, with editorial.
An advertisement that has the appearance of a news article or editorial, in a print publication and of course that includes websites.
It's been used for a long time and is often more effective than a straight forward advert although it takes more work. Publishers will often require the content written in house, their journalists and editors will in effect write an article about your service or products. Invariably biased in your favour. Most advertising agencies can produce this content too and in this case would work with the publisher's editors. Nearly all journals will reserve the right to publish only content they approve of.
Using advertorial is an opportunity to present aspects of your products and services that can not be covered in normal advertising. Partly due to cost, advertorials in effect use a large area of the journal so depending on when you need coverage, it may not be possible with a regular advert.
Publishers may see advertorial as a win win situation because the creation of content itself is a major expense. Hence, an advertorial supplied is (one would hope) generally more interesting to their readers and yet costs the publisher far less to produce.
Remember even though it's somewhat of an editorial feature, it is an advert and must follow advertising guidelines. It should include a clear indicator to the reader that it is in itself an advert. For small business especially if your business is based around personal consultations building a good relationship with publishers as an external specialist is also worth while since those articles on your own topics can help promote your business laterally. You may not receive payment for your editorial but when the publisher includes your contact details in the sign-off your article services the same purpose as an advertorial.