Neo4j is a graph database that stores relationships as first-class citizens, providing mission-critical context to data. It differs from traditional relational databases by storing data as graphs composed of nodes, labels, relationship types, and properties. In contrast, SQL-based databases require modeling relationships with additional tables and complex queries. Neo4j's approach enables effortless querying of relationships, reducing complexity and improving performance. The database allows users to specify relationship types in queries, providing a more natural way of expressing data connections.