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Update 2: Jim Wilson helps with the Understanding HBase and BigTable by explaining them from a "conceptual standpoint."
Update: InfoQ interview: HBase Leads Discuss Hadoop, BigTable and Distributed Databases. "MapReduce (both Google's and Hadoop's) is ideal for processing huge amounts of data with sizes that would not fit in a traditional database. Neither is appropriate for transaction/single request processing."

Hbase is the open source answer to BigTable, Google's highly scalable distributed database. It is built on top of Hadoop (product), which implements functionality similar to Google's GFS and Map/Reduce systems.