Did you read the Wikipedia page http://en.wikipedia.org/wiki/Hadoop ? It's a framework for processing large datasets in a distributed environment using the MapReduce algorithm from Google's paper http://labs.google.com/papers/mapreduce.html .

Hadoop implements the map reduce api. It is a full software stack that typically is taken to mean:

1 - hadoop proper: java code that implements the MR API;

1a - all the software to allow for job trackers, job retrying, job distribution, reporting, etc; across a cluster

1b - cascading / competitors that help you compose individual MR steps;

1c - task tracking and scheduling software such as the SNA projects from linkedin;

2 - a distributed file system called hdfs;

3 - binary file format code such as avro;

4 - various software that provide a sql like reporting api, such as hive, sawzall, pig, etc;

edit: and you might think the MR api is trivial (which is in some sense true), getting it somewhat right is a lot of work. Building software that will run on your 1 node dev box for development and run on a 6k node cluster is not a simple task. Neither is properly dealing with map/reduce task failure and retry while correctly removing the data that a partially complete task wrote.