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Neo4j is a graph database, so it models graphs. Here’s a picture of a graph:
The circles with numbers are the nodes. In Neo4j, they can contain any values, not just numbers. The edges are the lines between them (again, Neo4j allows arbitrary values on them). The edges represent relationships between the nodes.
In the case of DBpedia, the nodes are probably the articles and the edges are probably the links between articles. I’ve never heard of DBpedia before now, though, so I’m not sure on that.