(Full disclosure, I am one of the lead coordinators of the mapping effort discussed in the article and in my post below.)
Yes, the OpenStreetMap project is where the mapping is being done. The map linked in the article shows outbreak information overlaid on top of the OSM database of roads and buildings. It is this underlying map data that the croudsourcing is about.
If you go to this site you can create an OSM account and then start edititng the map immediately (think wikipedia, but for maps). You normally would edit by just going to the main OSM page and then editing the map there, the site I linked is the HOT task manager. We create areas on the task manager that need mapping done, the area is then broken up into a grid of small square tiles, and then people 'lock' a tile to work on, map all the roads and/or buildings in that tile, and finally mark the tile complete after the map has been updated. This tool was used to map all the roads and buildings in 3 large cities (Gueckedou, Macenta, and Kissidougou), where the outbreak originally started; all three of these towns were mapped completely, down to the last building, within 24 hours of HOT getting satellite imagery for them.
Right now the focus is to find and map all the small residential areas outside of these main cities, and to draw in the main connecting roads to each village. This helps the medical teams track the spread of the disease from village to village, as well as making it easier for them to travel around to do their own work. I really encourage slashdotters to help out on these kinds of projects. The mapping tools are easy to use (the in browser iD editor especially), but the technical knowledge of the slashdot crowd makes it easy for the average ./er to learn more advanced tools like JOSM and also to help with analysis and writing code to do cool stuff with the map data. You can really help out this (and a lot of other humanitarian efforts) by doing a bit of mapping anywhere in these areas, every little bit of extra data helps.
-AndrewBuck