The About page states:

LinkedGeoData uses the information collected by the OpenStreetMap project and makes it available as an RDF knowledge base according to the Linked Data principles. It interlinks this data with other knowledge bases in the Linking Open Data initiative.

RDF? That's, per wikipedia, "... a general method for conceptual description or modeling of information that is implemented in web resources..."

Linked Data principles? Again, per wikipedia, that's a "method of exposing, sharing, and connecting data via dereferenceable URIs on the Web." I looked up dereferenceable URI, too. It's "a resource retrieval mechanism that uses any of the internet protocols (e.g. HTTP) to obtain a copy or representation of the resource it identifies."

With all that as background, here's what's available at the project website, per the project blog:

LinkedGeoData is a comprehensive dataset derived from the OpenStreetMap database covering RDF descriptions of more than 350 million spatial features (i.e. nodes, ways, relations).

LinkedGeoData currently comprises RDF dumps, Linked Data and REST interfaces, links to DBpedia as well as a prototypical user interface for linked-geo-data browsing and authoring.

So, there's a dataset in RDF and some dev tools to access it, browse it and edit it. Oh, and you can download and use the dataset, too.

This all comes out of the The Research Group Agile Knowledge Engineering and Semantic Web (AKSW), hosted by the Department for Business-oriented Information Systems (BIS) of the Institute of Computer Science (IfI) / University of Leipzig. On its project page is the aim of the project:

The goal of this project is to publish OSM geo data, interlink it with other data sources and provide efficient means for browsing and authoring. We aim at working as closely as possible with both the OSM and LOD communities.

I conclude then, that project is about making OSM more useful for programmers and to provide tools to browse it and author in it.

The whole Linked Data idea is connected to the sematic Web; Tim Berners-Lee talked about it at TED (his talk) this spring.