Conflation (also map matching, map merging) involves combining map data from separate sources to create data that is better than either source on its own. A textbook definition is "[i]n GIS, conflation is defined as the process of combining geographic information from overlapping sources so as to retain accurate data, minimize redundancy, and reconcile data conflicts."  In the context of OpenStreetMap, it likely means taking government or non-profit data and merging it with existing OSM data. Some examples might be adding new roads from updated TIGER data, adding road surface details from a government source, or adding healthcare facilities provided by a non-profit governmental agency. Conflation is a form of importing, so please read the import guidelines before conflating other data sources with OSM.
Conflation can be performed manually via tools such as Potlatch and JOSM, may be semi-automated by plugins or features of editors (e.g. a JOSM plugin), or in some rare cases fully automated. There are some tips for manual conflation on the wiki.
While there are several commercial tools available for performing conflation, there are only two open source software that offer this capability. RoadMatcher is a tool that has been used with at least two OSM import projects, GeoBase in Canada and TPGInc in Albania. JCS Conflation Suite is an older (2003) tool from the same developers that hasn't been explored yet; perhaps RoadMatcher is simply a successor or perhaps it offers different functionality.
A group of researchers at the Centre for Geospatial Science, University of Nottingham, published a paper  discussing the conflation of Ordnance Survey data with OSM data. They used Python scripts in combination with QGIS to conflate data in Portsmouth, UK. In a related presentation  Jiang presents a good overview of the issues in conflating data. Attempts are being made to contact the author(s) to see if they are willing and able to share their work with the OSM community.
A group at the University of Texas, Arlington, have created a plugin for OpenJUMP to perform non-rigid conflation of vector datasets . Attempts are being made to contact the author(s) to see if they are willing and able to share their work with the OSM community.
- JOSM conflation plugin
- Potlatch 2 merging tool
- Manual conflation
- Osmsync point feature maintenance tool
- Longley, Paul A. et al (2001). Geographic Information Systems and Science. Wiley and Sons.
- Saalfield, Alan. Conflation: Automated Map Compilation. BUREAU OF THE CENSUS STATISTICAL RESEARCH DIVISION REPORT SERIES, SRD Research Report Number: Census/SRD/RR-87124. (report in PDF)
- Lynch, M. and A. Saalfeld, 1985, "Conflation: Automated Map Compilation, a Video Game Approach", Proceedings, Auto-Carto VII. (paper in PDF)
- Anand, Suchith; Morley, Jeremy; Jiang, Wenchao; Du, Heshan; Hart, Glen; Jackson, Mike. When worlds collide: combining Ordnance Survey and Open Street Map data. AGI GeoCommunity 2010. (paper, presentation)
- Jiang, Wenchao and Anand, Suchith. Map matching algorithm for data conflation – an open source approach
- Krishnamurthy, Ganesh; Devarajan, Venkat; Dragan, Irinel. Nonrigid Conflation for Vector Datasets Using EM Algorithm and Mixture of Gaussian Approach. Geoscience and Remote Sensing Symposium (IGARSS), 2010 IEEE International. (paper - requires IEEE subscription)