First Serial Rights
First serial rights means the writer offers a newspaper or magazine the right to publish the article, story or poem for the first time in any periodical. All other rights to the material remain with the writer. The qualifier "North American" is often added to this phrase to specify a geographical limit to the license.
When material is excerpted from a book scheduled to be published and it appears in a magazine or newspaper prior to book publication, this is also called first serial rights.
One-Time Rights
A periodical that licenses one-time rights to a work (also known as simultaneous rights) buys the nonexclusive right to publish the work once. That is, there is nothing to stop the author from selling the work to other publications at the same time. Simultaneous sales would typically be to periodicals without overlapping audiences.
Second Serial (Reprint) Rights
This gives a newspaper or magazine the opportunity to print an article, poem or story after it has already appeared in another newspaper or magazine. Second serial rights are nonexclusive—that is, they can be licensed to more than one market.
All Rights
This is just what it sounds like. If you license away all rights to your work, you forfeit the right to ever use it again. If you think you'll want to use the material later, you must avoid submitting to such markets or refuse payment and withdraw your material. Ask the editor whether he is willing to buy first rights instead of all rights before you agree to an assignment or sale. Some editors will reassign rights to a writer after a given period, such as one year. It's worth an inquiry in writing.
I took that all directly from the writer's market website. The magazine you are submitting your work to will tell you what rights they purchase. There's A TON of really useful info on the website, including more potential publishers than you will ever need. If you want access to the site, just drop me an e-mail or hit me up on AIM.
[ 30 January 2003: Message edited by: Benefit ]