"Mahout" is a Hindi term for a person who rides an elephant. The elephant, in this case, is Hadoop -- and Mahout is one of theĀ many projects that can sit on top of Hadoop, although you do not always need MapReduce to run it.
Mahout puts powerful mathematical tools in the hands of the mere mortal developers who write the InterWebs. It's a package of implementations of the most popular and important machine-learning algorithms, with the majority of the implementations designed specifically to use Hadoop to enable scalable processing of huge data sets. Some algorithms are available only in a nonparallelizable "serial" form due to the nature of the algorithm, but all can take advantage of HDFS for convenient access to data in your Hadoop processing pipeline.