Neo4j is a graph database that uses a labeled property graph model to store and query data. It allows for complex relationship queries using a simple declarative query language called Cypher. Data can be accessed and manipulated through a REST API or native graph database drivers. Common graph algorithms like centrality measures, minimum spanning trees, and community detection are available through Neo4j's algorithm library. The document provides examples of social network, movie recommendation, and IP mapping applications built using Neo4j.