Your Work has Been Seen and You are Contacted for a Advertorial
So you were successful in getting your work seen and a magazine contacts you for one of your images to use in advertising. An Advertorial may appear in the magazine as an advertisement, but is formatted to look like an editorial in terms of the magazines overall style.
The content of the Advertorial is typically not written or submitted by the advertising client, but rather the magazine iteself in order to make the advertising client look good. The material, and in this case your image, is then submitted to the advertising client for their approval at which time they may suggest (or require) changes.
Most photographers have a higher rate for advertising usage as opposed to editorial usage. After all, the advertising client may well have significant exposure relating to their product(s) depending upon the circulation of the magazine and the appeal of the article itself. The advertising client may also sell quite a few of their featured product if the magazine reaches their target audience.
An editorial on the other hand, is basically an opinion expressed by the magazine, which may or may not be favorable to a particular product or service. The magazine may in fact have a regular piece where it reviews products or services during each issue and may not simply feature a single service or product with each article rather compare several and issue an opinion on what may be a choice for its readers.
So, the magazine is looking to get a lower quote from you for the image that it is interested in purchasing. Another possibility is the magazine may want favorable usage rights ('unlimited') so that that it may potentially use your image in future publications for as long as the magazine remains in publication.
As you are contacted for the use of your work, it is important that you take the time to understand how you image will be used. If you are not sure, there are resources out their such as the Professional Photographers of America who may be able to shed some light on any questions that you may have.