Traversing a graph means visiting its nodes, following relationships according to some rules. In most cases only a subgraph is visited, as you already know where in the graph the interesting nodes and relationships are found.
Cypher provides a declarative way to query the graph powered by traversals and other techniques. See Cypher Query Language for more information.
Neo4j comes with a callback based traversal API which lets you specify the traversal rules. At a basic level there’s a choice between traversing breadth- or depth-first.