(Please read the full CMIS Page to get the state of the Nuxeo CMIS implementation.)
CMIS, for Content Management Interoperability Standard is a new standard that aims at making easier for third party software to interract with ECM software. The more Enterprise Content Management is seen as a service in your IT infrastructure, the more you need to standardize the code that gives access to your content, and that allows to contribute new one. This is where CMIS plays. Nuxeo belongs to the standardization comitee, you can see more on OASIS Website, and on Florent Guillaume's blogposts on CMIS.
In a nutshell, CMIS will give you a standard way for Create, Read, Update, Delete operations on document (plus all basic operations such a search, permission management). API will mostly be exposed through HTTP REST methods, but will also be provided as a java connector.
Nuxeo is working on an open source implementation which is following closely the standard as it evolves.