Non Relational is also known as NoSQL (not always SQL) provides a mechanism for storage and retrieval of data, which is modeled in means other than the tabular relations used in relational databases.
It is used to handle rapid growth of unstructured data and scale them out easily. This provides flexible schema so there is no such thing called Referential Integrity. The data are highly denormalized and do not require Joins between objects. It supports BASE (Basically Available Soft state, Eventual consistency). The BASE system loosened up the requirements on consistency to achieve better availability and partitioning for better scalability.
Examples : BigTable by Google, HBase by Yahoo, Cassandra by Facebook.