I suggest checking out the first video here: http://www.cloudera.com/hadoop-training-basic. It's a little more than 20 minutes long, and the lecturer talks about the problems that MapReduce and HDFS (Hadoop Distributed File System) are designed to solve.
If you're super curious about MapReduce and are down to spend a few hours learning about and playing around with Hadoop, most certainly check out the rest of the videos (you can leave out the ones about Hive) and work through the first two exercises -- the virtual machine they provide makes it very easy to implement and run your first MapReduce job. Doing this will answer your question better than anyone explaining it to you can. If you'd like to go even further and learn about how Hadoop works under the hood, buy the rough cuts version of Hadoop: The Definitive Guide here: http://oreilly.com/catalog/9780596521998/.
If you're super curious about MapReduce and are down to spend a few hours learning about and playing around with Hadoop, most certainly check out the rest of the videos (you can leave out the ones about Hive) and work through the first two exercises -- the virtual machine they provide makes it very easy to implement and run your first MapReduce job. Doing this will answer your question better than anyone explaining it to you can. If you'd like to go even further and learn about how Hadoop works under the hood, buy the rough cuts version of Hadoop: The Definitive Guide here: http://oreilly.com/catalog/9780596521998/.