Article syndication is the act of taking content that already exists on your site and giving it to another website to publish on their site.
Article syndication is most commonly done with blog articles, but content can also be syndicated across a whole site with the entirety of a site effectively being duplicated. This is obviously a contentious issue due to potential problems with duplicate content.
Syndicating content is most often done to get content in front of a larger audience and onto a site with a higher authority.
To avoid issues with duplicate content you should ensure that the partner site makes use of rel="canonical" tags or get them to noindex their copy. With either of these in place you will be far less likely to encounter problems with duplication.
If the partner is unwilling or unable to do this, maybe you should think about only allowing one of the sites to publish the content, either taking the content off of your site and giving it to the partner (this would be guest blogging) or keeping it for yourself.