Writing something at the specific request of an editor. Most writers start out, at least, by writing on speculation—meaning they send a query or manuscript to the publisher and the publisher agrees to buy it only after seeing it and deciding if he/she wants to buy it. There is no obligation to do so. The opposite of that is writing on assignment, which means the editor has asked you to write a specific article or story. You sometimes may get such an assignment if you send a query to the publisher and he responds that he'd like to assign you the piece you queried about. However, unless you have written for this editor in the past, he is likely to ask to see the piece on speculation—meaning he'll only buy it if he likes it. No obligation on his part.
In another scenario, he may come up with the idea for a piece and give you an assignment to write it. In this case he is saying he wants it—it won't be on speculation. However, if you write it and submit it, and he decides he doesn't like it or want it, he then has an obligation to reimburse you for your time with a kill fee.
In order to get writing assignments, you have to develop a reputation as a writer that does a certain kind of writing (such a feature articles), or that writes knowledgeably on a certain topic or topics (such as marriage). You will also want to sell regularly to publications interested in what you have to offer. Once they recognize what you have to offer, and they can see that you understand their publication and the needs of their readers, they will often come to you with those coveted assignments. Assigned articles typically pay at a higher rate than unsolicited ones. Many publications will raise that rate as you write for them more and more often. For 8 ways to land new writing assignments, go to: http://www.therenegadewriter.com/2012/04/19/8-ways-to-land-new-writing-assignments-not--queries.
Excerpt from "The Writing world Defined--A to Z" (stuartmarket.com)