SAP HANA combines database, data processing, and application platform capabilities in-memory. The platform provides libraries for predictive, planning, text processing, spatial, and business analytics. This new architecture enables converged OLTP and OLAP data processing within a single in-memory column-based data store with ACID compliance, while eliminating data redundancy and latency.
This is the official definition by SAP that can be found here http://www.saphana.com/community/about-hana.
However, for me HANA is an accelerator for presenting and predicting information. I am strongly recommending to enterprises to set up a HANA environment for small portion of their requirements.
For example weekly sales campains success monitoring for more than 100K customers by 300 SKUs, this might be a nightmare for any business analysts who are forced to be prepare reports 3-4 times a day. This is very good case if you are using SAP ERP and SAP BW. Just set up a HANA instance and get related sales data by using DXC method. ( Direct Exractor Connection – which helps you use existing datasources, but with latency unfortunately). And model your analytic, calculation view(s) and easily publish information by using SAP Lumira.
Finally do not get lost in HANA. Just start to establish with HANA. This is my way through HANA.